# Least common multiple

Least common multiple
You are encouraged to solve this task according to the task description, using any language you may know.

Compute the least common multiple of two integers.

Given   m   and   n,   the least common multiple is the smallest positive integer that has both   m   and   n   as factors.

Example

The least common multiple of 12 and 18 is 36, because 12 is a factor (12 × 3 = 36), and 18 is a factor (18 × 2 = 36), and there is no positive integer less than 36 that has both factors.   As a special case, if either   m   or   n   is zero, then the least common multiple is zero.

One way to calculate the least common multiple is to iterate all the multiples of   m,   until you find one that is also a multiple of   n.

If you already have   gcd   for greatest common divisor,   then this formula calculates   lcm.

${\displaystyle \operatorname {lcm} (m,n)={\frac {|m\times n|}{\operatorname {gcd} (m,n)}}}$

One can also find   lcm   by merging the prime decompositions of both   m   and   n.

## 8th

 : gcd \ a b -- gcd	dup 0 n:= if drop ;; then	tuck \ b a b	n:mod \ b a-mod-b	recurse ; 	 : lcm \ m n 	2dup \ m n m n	n:* \ m n m*n	n:abs \ m n abs(m*n)	-rot \ abs(m*n) m n 	gcd \ abs(m*n) gcd(m.n)	n:/mod \ abs / gcd 	nip \ abs div gcd; : demo \ n m -- 	2dup "LCM of " . . " and " . . " = " . lcm . ;	 12 18 demo cr-6 14 demo cr35  0 demo cr  bye
Output:
LCM of 18 and 12 = 36
LCM of 14 and -6 = 42
LCM of 0 and 35 = 0


with Ada.Text_IO; use Ada.Text_IO; procedure Lcm_Test is   function Gcd (A, B : Integer) return Integer is      M : Integer := A;      N : Integer := B;      T : Integer;   begin      while N /= 0 loop         T := M;         M := N;         N := T mod N;      end loop;      return M;   end Gcd;    function Lcm (A, B : Integer) return Integer is   begin      if A = 0 or B = 0 then         return 0;      end if;      return abs (A) * (abs (B) / Gcd (A, B));   end Lcm;begin   Put_Line ("LCM of 12, 18 is" & Integer'Image (Lcm (12, 18)));   Put_Line ("LCM of -6, 14 is" & Integer'Image (Lcm (-6, 14)));   Put_Line ("LCM of 35, 0 is" & Integer'Image (Lcm (35, 0)));end Lcm_Test;

Output:

LCM of 12, 18 is 36
LCM of -6, 14 is 42
LCM of 35, 0 is 0

## ALGOL 68

 BEGIN   PROC gcd = (INT m, n) INT :   BEGIN      INT a := ABS m, b := ABS n;      IF a=0 OR b=0 THEN 0 ELSE	 WHILE b /= 0 DO INT t = b; b := a MOD b; a := t OD;	 a      FI   END;   PROC lcm = (INT m, n) INT : ( m*n = 0 | 0 | ABS (m*n) % gcd (m, n));   INT m=12, n=18;   printf (($gxg(0)3(xgxg(0))l$,	    "The least common multiple of", m, "and", n, "is", lcm(m,n),	    "and their greatest common divisor is", gcd(m,n)))END
Output:
The least common multiple of 12 and 18 is 36 and their greatest common divisor is 6



Note that either or both PROCs could just as easily be implemented as OPs but then the operator priorities would also have to be declared.

## ALGOL W

begin    integer procedure gcd ( integer value a, b ) ;        if b = 0 then a else gcd( b, a rem abs(b) );     integer procedure lcm( integer value a, b ) ;        abs( a * b ) div gcd( a, b );     write( lcm( 15, 20  ) );end.

## APL

APL provides this function.

      12^1836

If for any reason we wanted to reimplement it, we could do so in terms of the greatest common divisor by transcribing the formula set out in the task specification into APL notation:

      LCM←{(|⍺×⍵)÷⍺∨⍵}      12 LCM 1836

## AppleScript

-- LEAST COMMON MULTIPLE ----------------------------------------------------- -- lcm :: Integral a => a -> a -> aon lcm(x, y)    if x = 0 or y = 0 then        0    else        abs(x div (gcd(x, y)) * y)    end ifend lcm  -- TEST ----------------------------------------------------------------------on run     lcm(12, 18)     --> 36end run -- GENERIC FUNCTIONS --------------------------------------------------------- -- abs :: Num a => a -> aon abs(x)    if x < 0 then        -x    else        x    end ifend abs -- gcd :: Integral a => a -> a -> aon gcd(x, y)    script        on |λ|(a, b)            if b = 0 then                a            else                |λ|(b, a mod b)            end if        end |λ|    end script     result's |λ|(abs(x), abs(y))end gcd
Output:
36

## Arendelle

For GCD function check out here

< a , b >

( return ,

abs ( @a * @b ) /
!gcd( @a , @b )

)

## Assembly

### x86 Assembly

 ; lcm.asm: calculates the least common multiple; of two positive integers;; nasm x86_64 assembly (linux) with libc; assemble: nasm -felf64 lcm.asm; gcc lcm.o; usage: ./a.out [number1] [number2]     global main    extern printf ; c function: prints formatted output    extern strtol ; c function: converts strings to longs     section .text main:    push rbp    ; set up stack frame     ; rdi contains argc    ; if less than 3, exit    cmp rdi, 3    jl incorrect_usage     ; push first argument as number    push rsi    mov rdi, [rsi+8]    mov rsi, 0    mov rdx, 10 ; base 10    call strtol    pop rsi    push rax     ; push second argument as number    push rsi    mov rdi, [rsi+16]    mov rsi, 0    mov rdx, 10 ; base 10    call strtol    pop rsi    push rax     ; pop arguments and call get_gcd    pop rdi    pop rsi    call get_gcd     ; print value    mov rdi, print_number    mov rsi, rax    call printf     ; exit    mov rax, 0  ; 0--exit success    pop rbp    ret incorrect_usage:    mov rdi, bad_use_string    ; rsi already contains argv    mov rsi, [rsi]    call printf    mov rax, 0  ; 0--exit success    pop rbp    ret bad_use_string:    db "Usage: %s [number1] [number2]",10,0 print_number:    db "%d",10,0 get_gcd:    push rbp    ; set up stack frame    mov rax, 0    jmp loop loop:    ; keep adding the first argument    ; to itself until a multiple    ; is found. then, return    add rax, rdi    push rax    mov rdx, 0    div rsi    cmp rdx, 0    pop rax    je gcd_found    jmp loop gcd_found:    pop rbp         ret

## AutoHotkey

LCM(Number1,Number2){ If (Number1 = 0 || Number2 = 0)  Return Var := Number1 * Number2 While, Number2  Num := Number2, Number2 := Mod(Number1,Number2), Number1 := Num Return, Var // Number1} Num1 = 12Num2 = 18MsgBox % LCM(Num1,Num2)

12 18
36
-6 14
42
35 0
0


## BASIC

### Applesoft BASIC

ported from BBC BASIC

10 DEF FN MOD(A) = INT((A / B - INT(A / B)) * B + .05) * SGN(A / B)20 INPUT"M=";M%30 INPUT"N=";N%40 GOSUB 10050 PRINT R60 END 100 REM LEAST COMMON MULTIPLE M% N%110 R = 0120 IF M% = 0 OR N% = 0 THEN RETURN130 A% = M% : B% = N% : GOSUB 200"GCD140 R = ABS(M%*N%)/R150 RETURN 200 REM GCD ITERATIVE EUCLID A% B%210 FOR B = B% TO 0 STEP 0220     C% = A%230     A% = B240     B = FN MOD(C%)250 NEXT B260 R = ABS(A%)270 RETURN

### BBC BASIC

       DEF FN_LCM(M%,N%)      IF M%=0 OR N%=0 THEN =0 ELSE =ABS(M%*N%)/FN_GCD_Iterative_Euclid(M%, N%)       DEF FN_GCD_Iterative_Euclid(A%, B%)      LOCAL C%      WHILE B%        C% = A%        A% = B%        B% = C% MOD B%      ENDWHILE      = ABS(A%)

### IS-BASIC

100 DEF LCM(A,B)=(A*B)/GCD(A,B)110 DEF GCD(A,B)120   DO WHILE B>0130     LET T=B:LET B=MOD(A,B):LET A=T140   LOOP 150   LET GCD=A160 END DEF 170 PRINT LCM(12,18)

## Batch File

@echo offsetlocal enabledelayedexpansionset num1=12set num2=18 call :lcm %num1% %num2%exit /b :lcm <input1> <input2>if %2 equ 0 (	set /a lcm = %num1%*%num2%/%1	echo LCM = !lcm!	pause>nul	goto :EOF)set /a res = %1 %% %2call :lcm %2 %res%goto :EOF
Output:
LCM = 36

## bc

Translation of: AWK
/* greatest common divisor */define g(m, n) {	auto t 	/* Euclid's method */	while (n != 0) {		t = m		m = n		n = t % n	}	return (m)} /* least common multiple */define l(m, n) {	auto r 	if (m == 0 || n == 0) return (0)	r = m * n / g(m, n)	if (r < 0) return (-r)	return (r)}

## Befunge

Inputs are limited to signed 16-bit integers.

&>:02*1-*:&>:#@!#._:02*1v>28*:*:**+:28*>:*:*/\:vv*-<|<:%/*:*:*82\%*:*:*82<<>28v>$/28*:*:*/*[email protected]^82::+**:*:*< Input: 12345 -23044 Output: 345660 ## Bracmat We utilize the fact that Bracmat simplifies fractions (using Euclid's algorithm). The function den$number returns the denominator of a number.

(gcd=  a b.   !arg:(?a.?b)  &   den$(!a*!b^-1) * (!a:<0&-1|1) * !a);out$(gcd$(12.18) gcd$(-6.14) gcd$(35.0) gcd$(117.18))

Output:

36 42 35 234

## Brat

 gcd = { a, b |  true? { a == 0 }    { b }     { gcd(b % a, a) }} lcm = { a, b |   a * b / gcd(a, b)} p lcm(12, 18) # 36p lcm(14, 21) # 42

## C

#include <stdio.h> int gcd(int m, int n){        int tmp;        while(m) { tmp = m; m = n % m; n = tmp; }               return n;} int lcm(int m, int n){        return m / gcd(m, n) * n;} int main(){        printf("lcm(35, 21) = %d\n", lcm(21,35));        return 0;}

## C++

Library: Boost
#include <boost/math/common_factor.hpp>#include <iostream> int main( ) {   std::cout << "The least common multiple of 12 and 18 is " <<       boost::math::lcm( 12 , 18 ) << " ,\n"      << "and the greatest common divisor " << boost::math::gcd( 12 , 18 ) << " !" << std::endl ;   return 0 ;}
Output:
The least common multiple of 12 and 18 is 36 ,
and the greatest common divisor 6 !


### Alternate solution

Works with: C++11
 #include <cstdlib>#include <iostream>#include <tuple> int gcd(int a, int b) {    a = abs(a);    b = abs(b);    while (b != 0) {        std::tie(a, b) = std::make_tuple(b, a % b);    }    return a;} int lcm(int a, int b) {    int c = gcd(a, b);    return c == 0 ? 0 : a / c * b;} int main() {    std::cout << "The least common multiple of 12 and 18 is " << lcm(12, 18) << ",\n"        << "and their greatest common divisor is " << gcd(12, 18) << "!"         << std::endl;    return 0;}

## C#

Using System;class Program{    static int gcd(int m, int n)    {        return n == 0 ? Math.Abs(m) : gcd(n, n % m);    }    static int lcm(int m, int n)    {        return Math.Abs(m * n) / gcd(m, n);    }    static void Main()    {        Console.WriteLine("lcm(12,18)=" + lcm(12,18));    }}
Output:
lcm(12,18)=36

## Clojure

(defn gcd       [a b]      (if (zero? b)      a      (recur b, (mod a b)))) (defn lcm       [a b]      (/ (* a b) (gcd a b)));; to calculate the lcm for a variable number of arguments(defn lcmv [& v] (reduce lcm v))

## COBOL

       IDENTIFICATION DIVISION.       PROGRAM-ID. show-lcm.        ENVIRONMENT DIVISION.       CONFIGURATION SECTION.       REPOSITORY.           FUNCTION lcm           .       PROCEDURE DIVISION.           DISPLAY "lcm(35, 21) = " FUNCTION lcm(35, 21)           GOBACK           .       END PROGRAM show-lcm.        IDENTIFICATION DIVISION.       FUNCTION-ID. lcm.        ENVIRONMENT DIVISION.       CONFIGURATION SECTION.       REPOSITORY.           FUNCTION gcd           .       DATA DIVISION.       LINKAGE SECTION.       01  m                       PIC S9(8).       01  n                       PIC S9(8).       01  ret                     PIC S9(8).        PROCEDURE DIVISION USING VALUE m, n RETURNING ret.           COMPUTE ret = FUNCTION ABS(m * n) / FUNCTION gcd(m, n)           GOBACK           .       END FUNCTION lcm.        IDENTIFICATION DIVISION.       FUNCTION-ID. gcd.        DATA DIVISION.       LOCAL-STORAGE SECTION.       01  temp                    PIC S9(8).        01  x                       PIC S9(8).       01  y                       PIC S9(8).        LINKAGE SECTION.       01  m                       PIC S9(8).       01  n                       PIC S9(8).       01  ret                     PIC S9(8).        PROCEDURE DIVISION USING VALUE m, n RETURNING ret.           MOVE m to x           MOVE n to y            PERFORM UNTIL y = 0               MOVE x TO temp               MOVE y TO x               MOVE FUNCTION MOD(temp, y) TO Y           END-PERFORM            MOVE FUNCTION ABS(x) TO ret           GOBACK           .       END FUNCTION gcd.

## Common Lisp

Common Lisp provides the lcm function. It can accept two or more (or less) parameters.

CL-USER> (lcm 12 18)36CL-USER> (lcm 12 18 22)396

Here is one way to reimplement it.

CL-USER> (defun my-lcm (&rest args)	   (reduce (lambda (m n)		     (cond ((or (= m 0) (= n 0)) 0)			   (t (abs (/ (* m n) (gcd m n))))))		   args :initial-value 1))MY-LCMCL-USER> (my-lcm 12 18)36CL-USER> (my-lcm 12 18 22)396

In this code, the lambda finds the least common multiple of two integers, and the reduce transforms it to accept any number of parameters. The reduce operation exploits how lcm is associative, (lcm a b c) == (lcm (lcm a b) c); and how 1 is an identity, (lcm 1 a) == a.

## D

import std.stdio, std.bigint, std.math; T gcd(T)(T a, T b) pure nothrow {    while (b) {        immutable t = b;        b = a % b;        a = t;    }    return a;} T lcm(T)(T m, T n) pure nothrow {    if (m == 0) return m;    if (n == 0) return n;    return abs((m * n) / gcd(m, n));} void main() {    lcm(12, 18).writeln;    lcm("2562047788015215500854906332309589561".BigInt,        "6795454494268282920431565661684282819".BigInt).writeln;}
Output:
36
15669251240038298262232125175172002594731206081193527869

## DWScript

PrintLn(Lcm(12, 18));

Output:

36

 main() {	int x=8;  int y=12;int z= gcd(x,y);  var lcm=(x*y)/z;  print('$lcm'); } int gcd(int a,int b){ if(b==0) return a; if(b!=0) return gcd(b,a%b);}  ## EchoLisp (lcm a b) is already here as a two arguments function. Use foldl to find the lcm of a list of numbers.  (lcm 0 9) → 0(lcm 444 888)→ 888(lcm 888 999) → 7992 (define (lcm* list) (foldl lcm (first list) list)) → lcm*(lcm* '(444 888 999)) → 7992  ## Elena Translation of: C# ELENA 3.4 : import extensions.import system'math. gcd = (:m:n)((n == 0)iif(m absolute,$(gcd(n,n mod:m)))). lcm = (:m:n)((m * n) absolute / gcd(m,n)). public program[    console printLine("lcm(12,18)=",lcm(12,18)).]
Output:
lcm(12,18)=36


## Elixir

defmodule RC do  def gcd(a,0), do: abs(a)  def gcd(a,b), do: gcd(b, rem(a,b))   def lcm(a,b), do: div(abs(a*b), gcd(a,b))end IO.puts RC.lcm(-12,15)
Output:
60


## Erlang

% Implemented by Arjun Sunel-module(lcm).-export([main/0]). main() ->	lcm(-3,4). gcd(A, 0) -> 	A; gcd(A, B) -> 	gcd(B, A rem B). lcm(A,B) ->	abs(A*B div gcd(A,B)).
Output:
12


## ERRE

PROGRAM LCM PROCEDURE GCD(A,B->GCD)    LOCAL C    WHILE B DO        C=A        A=B        B=C MOD B    END WHILE    GCD=ABS(A)END PROCEDURE PROCEDURE LCM(M,N->LCM)    IF M=0 OR N=0 THEN         LCM=0        EXIT PROCEDURE      ELSE         GCD(M,N->GCD)        LCM=ABS(M*N)/GCD    END IFEND PROCEDURE BEGIN    LCM(18,12->LCM)    PRINT("LCM of 18 AND 12 =";LCM)    LCM(14,-6->LCM)    PRINT("LCM of 14 AND -6 =";LCM)    LCM(0,35->LCM)    PRINT("LCM of 0 AND 35 =";LCM)END PROGRAM
Output:
LCM of 18 and 12 = 36
LCM of 14 and -6 = 42
LCM of 0 and 35 = 0


## Euphoria

function gcd(integer m, integer n)    integer tmp    while m do        tmp = m        m = remainder(n,m)        n = tmp    end while    return nend function function lcm(integer m, integer n)    return m / gcd(m, n) * nend function

## Excel

Excel's LCM can handle multiple values. Type in a cell:

=LCM(A1:J1)

This will get the LCM on the first 10 cells in the first row. Thus :

12	3	5	23	13	67	15	9	4	2

3605940

## Ezhil

 ## இந்த நிரல் இரு எண்களுக்கு இடையிலான மீச்சிறு பொது மடங்கு (LCM), மீப்பெரு பொது வகுத்தி (GCD) என்ன என்று கணக்கிடும் நிரல்பாகம் மீபொம(எண்1, எண்2) 	@(எண்1 == எண்2) ஆனால்   ## இரு எண்களும் சமம் என்பதால், மீபொம அந்த எண்ணேதான் 		பின்கொடு எண்1 	@(எண்1 > எண்2) இல்லைஆனால் 		சிறியது = எண்2		பெரியது = எண்1 	இல்லை 		சிறியது = எண்1		பெரியது = எண்2 	முடி 	மீதம் = பெரியது % சிறியது 	@(மீதம் == 0) ஆனால்   ## பெரிய எண்ணில் சிறிய எண் மீதமின்றி வகுபடுவதால், பெரிய எண்தான் மீபொம 		பின்கொடு பெரியது 	இல்லை 		தொடக்கம் = பெரியது + 1		நிறைவு = சிறியது * பெரியது 		@(எண் = தொடக்கம், எண் <= நிறைவு, எண் = எண் + 1) ஆக     ## ஒவ்வோர் எண்ணாக எடுத்துக்கொண்டு தரப்பட்ட இரு எண்களாலும் வகுத்துப் பார்க்கின்றோம். முதலாவதாக இரண்டாலும் மீதமின்றி வகுபடும் எண்தான் மீபொம 			மீதம்1 = எண் % சிறியது			மீதம்2 = எண் % பெரியது 			@((மீதம்1 == 0) && (மீதம்2 == 0)) ஆனால்				பின்கொடு எண்			முடி 		முடி 	முடி	 முடி அ = int(உள்ளீடு("ஓர் எண்ணைத் தாருங்கள் "))ஆ = int(உள்ளீடு("இன்னோர் எண்ணைத் தாருங்கள் ")) பதிப்பி "நீங்கள் தந்த இரு எண்களின் மீபொம (மீச்சிறு பொது மடங்கு, LCM) = ", மீபொம(அ, ஆ)

## F#

let rec gcd x y = if y = 0 then abs x else gcd y (x % y) let lcm x y = x * y / (gcd x y)

## Factor

The vocabulary math.functions already provides lcm.

USING: math.functions prettyprint ;26 28 lcm .

This program outputs 364.

One can also reimplement lcm.

USING: kernel math prettyprint ;IN: script : gcd ( a b -- c )    [ abs ] [        [ nip ] [ mod ] 2bi gcd    ] if-zero ; : lcm ( a b -- c )    [ * abs ] [ gcd ] 2bi / ; 26 28 lcm .

## Forth

: gcd ( a b -- n )  begin dup while tuck mod repeat drop ; : lcm ( a b -- n )  over 0= over 0= or if 2drop 0 exit then  2dup gcd abs */ ;

## Fortran

This solution is written as a combination of 2 functions, but a subroutine implementation would work great as well.

     integer function lcm(a,b)    integer:: a,b        lcm = a*b / gcd(a,b)    end function lcm     integer function gcd(a,b)    integer :: a,b,t        do while (b/=0)            t = b            b = mod(a,b)            a = t        end do        gcd = abs(a)    end function gcd

## FreeBASIC

' FB 1.05.0 Win64 Function lcm (m As Integer, n As Integer) As Integer  If m = 0 OrElse n = 0 Then Return 0  If m < n Then Swap m, n '' to minimize iterations needed  Var count = 0  Do    count +=1  Loop Until (m * count) Mod n  = 0  Return m * countEnd Function Print "lcm(12, 18) ="; lcm(12, 18)Print "lcm(15, 12) ="; lcm(15, 12)Print "lcm(10, 14) ="; lcm(10, 14)PrintPrint "Press any key to quit"Sleep
Output:
lcm(12, 18) = 36
lcm(15, 12) = 60
lcm(10, 14) = 70


## Frink

Frink has a built-in LCM function that handles arbitrarily-large integers.

 println[lcm[2562047788015215500854906332309589561, 6795454494268282920431565661684282819]]

## FunL

FunL has function lcm in module integers with the following definition:

def  lcm( _, 0 ) =  0  lcm( 0, _ ) =  0  lcm( x, y ) =  abs( (x\gcd(x, y)) y )

## GAP

# Built-inLcmInt(12, 18);# 36

## Go

package main import (    "fmt"    "math/big") var m, n, z big.Int func init() {    m.SetString("2562047788015215500854906332309589561", 10)    n.SetString("6795454494268282920431565661684282819", 10)} func main() {    fmt.Println(z.Mul(z.Div(&m, z.GCD(nil, nil, &m, &n)), &n))}
Output:
15669251240038298262232125175172002594731206081193527869


## Groovy

def gcdgcd = { m, n -> m = m.abs(); n = n.abs(); n == 0 ? m : m%n == 0 ? n : gcd(n, m % n) } def lcd = { m, n -> Math.abs(m * n) / gcd(m, n) } [[m: 12, n: 18, l: 36], [m: -6, n: 14, l: 42], [m: 35, n: 0, l: 0]].each { t ->    println "LCD of $t.m,$t.n is $t.l" assert lcd(t.m, t.n) == t.l} Output: LCD of 12, 18 is 36 LCD of -6, 14 is 42 LCD of 35, 0 is 0 ## GW-BASIC Translation of: C Works with: PC-BASIC version any 10 PRINT "LCM(35, 21) = ";20 LET MLCM = 3530 LET NLCM = 2140 GOSUB 200: ' Calculate LCM50 PRINT LCM60 END 195 ' Calculate LCM200 LET MGCD = MLCM210 LET NGCD = NLCM 220 GOSUB 400: ' Calculate GCD 230 LET LCM = MLCM / GCD * NLCM240 RETURN 395 ' Calculate GCD400 WHILE MGCD <> 0410 LET TMP = MGCD420 LET MGCD = NGCD MOD MGCD430 LET NGCD = TMP440 WEND450 LET GCD = NGCD460 RETURN  ## Haskell That is already available as the function lcm in the Prelude. Here's the implementation: lcm :: (Integral a) => a -> a -> alcm _ 0 = 0lcm 0 _ = 0lcm x y = abs ((x quot (gcd x y)) * y) ## Icon and Unicon The lcm routine from the Icon Programming Library uses gcd. The routine is link numbers procedure main()write("lcm of 18, 36 = ",lcm(18,36))write("lcm of 0, 9 36 = ",lcm(0,9))end numbers provides lcm and gcd and looks like this: procedure lcm(i, j) #: least common multiple if (i = 0) | (j = 0) then return 0 return abs(i * j) / gcd(i, j)end ## J J provides the dyadic verb *. which returns the least common multiple of its left and right arguments.  12 *. 1836 12 *. 18 2236 132 *./ 12 18 22396 0 1 0 1 *. 0 0 1 1 NB. for truth valued arguments (0 and 1) it is equivalent to "and"0 0 0 1 *./~ 0 10 00 1 Note: least common multiple is the original boolean multiplication. Constraining the universe of values to 0 and 1 allows us to additionally define logical negation (and boolean algebra was redefined to include this constraint in the early 1900s - the original concept of boolean algebra is now known as a boolean ring). ## Java import java.util.Scanner; public class LCM{ public static void main(String[] args){ Scanner aScanner = new Scanner(System.in); //prompts user for values to find the LCM for, then saves them to m and n System.out.print("Enter the value of m:"); int m = aScanner.nextInt(); System.out.print("Enter the value of n:"); int n = aScanner.nextInt(); int lcm = (n == m || n == 1) ? m :(m == 1 ? n : 0); /* this section increases the value of mm until it is greater / than or equal to nn, then does it again when the lesser / becomes the greater--if they aren't equal. If either value is 1, / no need to calculate*/ if (lcm == 0) { int mm = m, nn = n; while (mm != nn) { while (mm < nn) { mm += m; } while (nn < mm) { nn += n; } } lcm = mm; } System.out.println("lcm(" + m + ", " + n + ") = " + lcm); }} ## JavaScript ### ES5 Computing the least common multiple of an integer array, using the associative law: ${\displaystyle \operatorname {lcm} (a,b,c)=\operatorname {lcm} (\operatorname {lcm} (a,b),c),}$ ${\displaystyle \operatorname {lcm} (a_{1},a_{2},\ldots ,a_{n})=\operatorname {lcm} (\operatorname {lcm} (a_{1},a_{2},\ldots ,a_{n-1}),a_{n}).}$ function LCM(A) // A is an integer array (e.g. [-50,25,-45,-18,90,447]){ var n = A.length, a = Math.abs(A[0]); for (var i = 1; i < n; i++) { var b = Math.abs(A[i]), c = a; while (a && b){ a > b ? a %= b : b %= a; } a = Math.abs(c*A[i])/(a+b); } return a;} /* For example: LCM([-50,25,-45,-18,90,447]) -> 67050*/ ### ES6 Translation of: Haskell (() => { 'use strict'; // gcd :: Integral a => a -> a -> a let gcd = (x, y) => { let _gcd = (a, b) => (b === 0 ? a : _gcd(b, a % b)), abs = Math.abs; return _gcd(abs(x), abs(y)); } // lcm :: Integral a => a -> a -> a let lcm = (x, y) => x === 0 || y === 0 ? 0 : Math.abs(Math.floor(x / gcd(x, y)) * y); // TEST return lcm(12, 18); })(); Output: 36 ## jq Direct method # Define the helper function to take advantage of jq's tail-recursion optimizationdef lcm(m; n): def _lcm: # state is [m, n, i] if (.[2] % .[1]) == 0 then .[2] else (.[0:2] + [.[2] + m]) | _lcm end; [m, n, m] | _lcm;  ## Julia Built-in function: lcm(m,n) ## K  gcd:{:[~x;y;_f[y;x!y]]} lcm:{_abs _ x*y%gcd[x;y]} lcm .'(12 18; -6 14; 35 0)36 42 0 lcm/1+!20232792560 ## Kotlin fun main(args: Array<String>) { fun gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b) fun lcm(a: Int, b: Int) = a * b / gcd(a, b) println(lcm(15, 9))}  ## LabVIEW Requires GCD. This image is a VI Snippet, an executable image of LabVIEW code. The LabVIEW version is shown on the top-right hand corner. You can download it, then drag-and-drop it onto the LabVIEW block diagram from a file browser, and it will appear as runnable, editable code. ## Lasso define gcd(a,b) => { while(#b != 0) => { local(t = #b) #b = #a % #b #a = #t } return #a}define lcm(m,n) => { #m == 0 || #n == 0 ? return 0 local(r = (#m * #n) / decimal(gcd(#m, #n))) return integer(#r)->abs} lcm(-6, 14)lcm(2, 0)lcm(12, 18)lcm(12, 22)lcm(7, 31) Output: 42 0 36 132 217 ## Liberty BASIC print "Least Common Multiple of 12 and 18 is ";LCM(12,18)end function LCM(m,n) LCM=abs(m*n)/GCD(m,n) end function function GCD(a,b) while b c = a a = b b = c mod b wend GCD = abs(a) end function  ## Logo to abs :n output sqrt product :n :nend to gcd :m :n output ifelse :n = 0 [ :m ] [ gcd :n modulo :m :n ]end to lcm :m :n output quotient (abs product :m :n) gcd :m :nend Demo code: print lcm 38 46 Output: 874 ## Lua function gcd( m, n ) while n ~= 0 do local q = m m = n n = q % n end return mend function lcm( m, n ) return ( m ~= 0 and n ~= 0 ) and m * n / gcd( m, n ) or 0end print( lcm(12,18) ) ## Maple The least common multiple of two integers is computed by the built-in procedure ilcm in Maple. This should not be confused with lcm, which computes the least common multiple of polynomials. > ilcm( 12, 18 ); 36  ## Mathematica LCM[18,12]-> 36 ## MATLAB / Octave  lcm(a,b)  ## Maxima lcm(a, b); /* a and b may be integers or polynomials */ /* In Maxima the gcd of two integers is always positive, and a * b = gcd(a, b) * lcm(a, b),so the lcm may be negative. To get a positive lcm, simply do */ abs(lcm(a, b)) ## Microsoft Small Basic Translation of: C  Textwindow.Write("LCM(35, 21) = ")mlcm = 35nlcm = 21CalculateLCM()TextWindow.WriteLine(lcm) Sub CalculateLCM mgcd = mlcm ngcd = nlcm CalculateGCD() lcm = mlcm / gcd * nlcmEndSub Sub CalculateGCD While mgcd <> 0 tmp = mgcd mgcd = Math.Remainder(ngcd, mgcd) ngcd = tmp EndWhile gcd = ngcdEndSub  ## МК-61/52 ИПA ИПB * |x| ПC ИПA ИПB / [x] П9ИПA ИПB ПA ИП9 * - ПB x=0 05 ИПCИПA / С/П ## ML ### mLite fun gcd (a, 0) = a | (0, b) = b | (a, b) where (a < b) = gcd (a, b rem a) | (a, b) = gcd (b, a rem b) fun lcm (a, b) = let val d = gcd (a, b) in a * b div d end  ## Modula-2 Translation of: C Works with: ADW Modula-2 version any (Compile with the linker option Console Application).  MODULE LeastCommonMultiple; FROM STextIO IMPORT WriteString, WriteLn;FROM SWholeIO IMPORT WriteInt; PROCEDURE GCD(M, N: INTEGER): INTEGER;VAR Tmp: INTEGER;BEGIN WHILE M <> 0 DO Tmp := M; M := N MOD M; N := Tmp; END; RETURN N;END GCD; PROCEDURE LCM(M, N: INTEGER): INTEGER;BEGIN RETURN M / GCD(M, N) * N;END LCM; BEGIN WriteString("LCM(35, 21) = "); WriteInt(LCM(35, 21), 1); WriteLn;END LeastCommonMultiple.  ## NetRexx /* NetRexx */options replace format comments java crossref symbols nobinary numeric digits 3000 runSample(arg)return -- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~method lcm(m_, n_) public static L_ = m_ * n_ % gcd(m_, n_) return L_ -- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~-- Euclid's algorithm - iterative implementationmethod gcd(m_, n_) public static loop while n_ > 0 c_ = m_ // n_ m_ = n_ n_ = c_ end return m_ -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~method runSample(arg) private static parse arg samples if samples = '' | samples = '.' then samples = '-6 14 = 42 |' - '3 4 = 12 |' - '18 12 = 36 |' - '2 0 = 0 |' - '0 85 = 0 |' - '12 18 = 36 |' - '5 12 = 60 |' - '12 22 = 132 |' - '7 31 = 217 |' - '117 18 = 234 |' - '38 46 = 874 |' - '18 12 -5 = 180 |' - '-5 18 12 = 180 |' - -- confirm that other permutations work '12 -5 18 = 180 |' - '18 12 -5 97 = 17460 |' - '30 42 = 210 |' - '30 42 = . |' - -- 210; no verification requested '18 12' -- 36 loop while samples \= '' parse samples sample '|' samples loop while sample \= '' parse sample mnvals '=' chk sample if chk = '' then chk = '.' mv = mnvals.word(1) loop w_ = 2 to mnvals.words mnvals nv = mnvals.word(w_) mv = mv.abs nv = nv.abs mv = lcm(mv, nv) end w_ lv = mv select case chk when '.' then state = '' when lv then state = '(verified)' otherwise state = '(failed)' end mnvals = mnvals.space(1, ',').changestr(',', ', ') say 'lcm of' mnvals.right(15.max(mnvals.length)) 'is' lv.right(5.max(lv.length)) state end end return  Output: lcm of -6, 14 is 42 (verified) lcm of 3, 4 is 12 (verified) lcm of 18, 12 is 36 (verified) lcm of 2, 0 is 0 (verified) lcm of 0, 85 is 0 (verified) lcm of 12, 18 is 36 (verified) lcm of 5, 12 is 60 (verified) lcm of 12, 22 is 132 (verified) lcm of 7, 31 is 217 (verified) lcm of 117, 18 is 234 (verified) lcm of 38, 46 is 874 (verified) lcm of 18, 12, -5 is 180 (verified) lcm of -5, 18, 12 is 180 (verified) lcm of 12, -5, 18 is 180 (verified) lcm of 18, 12, -5, 97 is 17460 (verified) lcm of 30, 42 is 210 (verified) lcm of 30, 42 is 210 lcm of 18, 12 is 36  ## Nim proc gcd(u, v): auto = var t = 0 u = u v = v while v != 0: t = u u = v v = t %% v abs(u) proc lcm(a, b): auto = abs(a * b) div gcd(a, b) echo lcm(12, 18)echo lcm(-6, 14) ## Objeck Translation of: C  class LCM { function : Main(args : String[]) ~ Nil { IO.Console->Print("lcm(35, 21) = ")->PrintLine(lcm(21,35)); } function : lcm(m : Int, n : Int) ~ Int { return m / gcd(m, n) * n; } function : gcd(m : Int, n : Int) ~ Int { tmp : Int; while(m <> 0) { tmp := m; m := n % m; n := tmp; }; return n; }}  ## OCaml let rec gcd u v = if v <> 0 then (gcd v (u mod v)) else (abs u) let lcm m n = match m, n with | 0, _ | _, 0 -> 0 | m, n -> abs (m * n) / (gcd m n) let () = Printf.printf "lcm(35, 21) = %d\n" (lcm 21 35) ## Oforth lcm is already defined into Integer class : 12 18 lcm ## ooRexx  say lcm(18, 12) -- calculate the greatest common denominator of a numerator/denominator pair::routine gcd private use arg x, y loop while y \= 0 -- check if they divide evenly temp = x // y x = y y = temp end return x -- calculate the least common multiple of a numerator/denominator pair::routine lcm private use arg x, y return x / gcd(x, y) * y  ## Order Translation of: bc #include <order/interpreter.h> #define ORDER_PP_DEF_8gcd ORDER_PP_FN( \8fn(8U, 8V, \ 8if(8isnt_0(8V), 8gcd(8V, 8remainder(8U, 8V)), 8U))) #define ORDER_PP_DEF_8lcm ORDER_PP_FN( \8fn(8X, 8Y, \ 8if(8or(8is_0(8X), 8is_0(8Y)), \ 0, \ 8quotient(8times(8X, 8Y), 8gcd(8X, 8Y)))))// No support for negative numbers ORDER_PP( 8to_lit(8lcm(12, 18)) ) // 36 ## PARI/GP Built-in function: lcm ## Pascal Program LeastCommonMultiple(output); function lcm(a, b: longint): longint; begin lcm := a; while (lcm mod b) <> 0 do inc(lcm, a); end; begin writeln('The least common multiple of 12 and 18 is: ', lcm(12, 18));end. Output: The least common multiple of 12 and 18 is: 36  ## Perl Using GCD: sub gcd { my ($x, $y) = @_; while ($x) { ($x,$y) = ($y %$x, $x) }$y} sub lcm {	my ($x,$y) = @_;	($x &&$y) and $x / gcd($x, $y) *$y or 0} print lcm(1001, 221);
Or by repeatedly increasing the smaller of the two until LCM is reached:

## PicoLisp

Using 'gcd' from Greatest common divisor#PicoLisp:

(de lcm (A B)   (abs (*/ A B (gcd A B))) )

## PL/I

 /* Calculate the Least Common Multiple of two integers. */ LCM: procedure options (main);          /* 16 October 2013 */   declare (m, n) fixed binary (31);    get (m, n);   put edit ('The LCM of ', m, ' and ', n, ' is', LCM(m, n)) (a, x(1)); LCM: procedure (m, n) returns (fixed binary (31));   declare (m, n) fixed binary (31) nonassignable;    if m = 0 | n = 0 then return (0);   return (abs(m*n) / GCD(m, n));end LCM; GCD: procedure (a, b) returns (fixed binary (31)) recursive;   declare (a, b) fixed binary (31);    if b = 0 then return (a);    return (GCD (b, mod(a, b)) ); end GCD;end LCM;
The LCM of              14  and              35  is             70


## PowerShell

 function gcd ($a,$b)  {    function pgcd ($n,$m)  {        if($n -le$m) {             if($n -eq 0) {$m}            else{pgcd $n ($m-$n)} } else {pgcd$m $n} }$n = [Math]::Abs($a)$m = [Math]::Abs($b) (pgcd$n $m)}function lcm ($a, $b) { [Math]::Abs($a*$b)/(gcd$a $b)}lcm 12 18  ### version 2 version2 is faster than version1  function gcd ($a, $b) { function pgcd ($n, $m) { if($n -le $m) { if($n -eq 0) {$m} else{pgcd$n ($m%$n)}        }        else {pgcd $m$n}    }    $n = [Math]::Abs($a)    $m = [Math]::Abs($b)    (pgcd $n$m)}function lcm ($a,$b)  {    [Math]::Abs($a*$b)/(gcd $a$b)}lcm 12 18

Output:

36


## Prolog

SWI-Prolog knows gcd.

lcm(X, Y, Z) :-	Z is abs(X * Y) / gcd(X,Y).

Example:

 ?- lcm(18,12, Z).
Z = 36.


## PureBasic

Procedure GCDiv(a, b); Euclidean algorithm  Protected r  While b    r = b    b = a%b    a = r  Wend  ProcedureReturn aEndProcedure Procedure LCM(m,n)  Protected t  If m And n    t=m*n/GCDiv(m,n)  EndIf  ProcedureReturn t*Sign(t)EndProcedure

## Python

### gcd

Using the fractions libraries gcd function:

>>> import fractions>>> def lcm(a,b): return abs(a * b) / fractions.gcd(a,b) if a and b else 0 >>> lcm(12, 18)36>>> lcm(-6, 14)42>>> assert lcm(0, 2) == lcm(2, 0) == 0>>>

### Prime decomposition

This imports Prime decomposition#Python

from prime_decomposition import decomposetry:    reduceexcept NameError:    from functools import reduce def lcm(a, b):    mul = int.__mul__    if a and b:        da = list(decompose(abs(a)))        db = list(decompose(abs(b)))        merge= da        for d in da:            if d in db: db.remove(d)        merge += db        return reduce(mul, merge, 1)    return 0 if __name__ == '__main__':    print( lcm(12, 18) )    # 36    print( lcm(-6, 14) )    # 42    assert lcm(0, 2) == lcm(2, 0) == 0

### Iteration over multiples

>>> def lcm(*values):	values = set([abs(int(v)) for v in values])	if values and 0 not in values:		n = n0 = max(values)		values.remove(n)		while any( n % m for m in values ):			n += n0		return n	return 0 >>> lcm(-6, 14)42>>> lcm(2, 0)0>>> lcm(12, 18)36>>> lcm(12, 18, 22)396>>>

### Repeated modulo

Translation of: Tcl
>>> def lcm(p,q):	p, q = abs(p), abs(q)	m = p * q	if not m: return 0	while True:		p %= q		if not p: return m // q		q %= p		if not q: return m // p  >>> lcm(-6, 14)42>>> lcm(12, 18)36>>> lcm(2, 0)0>>>

## Qi

 (define gcd  A 0 -> A  A B -> (gcd B (MOD A B))) (define lcm A B -> (/ (* A B) (gcd A B)))

## R

 "%gcd%" <- function(u, v) {ifelse(u %% v != 0, v %gcd% (u%%v), v)} "%lcm%" <- function(u, v) { abs(u*v)/(u %gcd% v)} print (50 %lcm% 75)

## Racket

Racket already has defined both lcm and gcd funtions:

#lang racket(lcm 3 4 5 6)        ;returns 60(lcm 8 108)          ;returns 216(gcd 8 108)          ;returns 4(gcd 108 216 432)    ;returns 108

## Retro

This is from the math extensions library included with Retro.

: gcd ( ab-n ) [ tuck mod dup ] while drop ;: lcm ( ab-n ) 2over gcd [ * ] dip / ;

## REXX

### version 1

The   lcm   subroutine can handle any number of integers and/or arguments.

The integers (negative/zero/positive) can be (as per the   numeric digits)   up to ten thousand digits.

Usage note:   the integers can be expressed as a list and/or specified as individual arguments   (or as mixed).

/*REXX program finds the  LCM  (Least Common Multiple)  of any number of integers.      */numeric digits 10000                             /*can handle 10k decimal digit numbers.*/say 'the LCM of      19  and   0                   is ───►  '     lcm(19    0            )say 'the LCM of       0  and  85                   is ───►  '     lcm( 0   85            )say 'the LCM of      14  and  -6                   is ───►  '     lcm(14,  -6            )say 'the LCM of      18  and  12                   is ───►  '     lcm(18   12            )say 'the LCM of      18  and  12  and  -5          is ───►  '     lcm(18   12,   -5      )say 'the LCM of      18  and  12  and  -5  and  97 is ───►  '     lcm(18,  12,   -5,   97)say 'the LCM of 2**19-1  and  2**521-1             is ───►  '     lcm(2**19-1    2**521-1)                                                 /* [↑]   7th  &  13th  Mersenne primes.*/exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/lcm: procedure; parse arg $,_;$=$_; do i=3 to arg();$=$arg(i); end /*i*/ parse var$ x $/*obtain the first value in args. */ x=abs(x) /*use the absolute value of X. */ do while$\==''                       /*process the remainder of args.  */               parse var $!$;    if !<0  then !=-!  /*pick off the next arg (ABS val).*/               if !==0  then return 0                 /*if zero, then LCM is also zero. */               d=x*!                                  /*calculate part of the LCM here. */                      do  until !==0;    parse  value   x//!  !     with     !  x                      end   /*until*/                 /* [↑]  this is a short & fast GCD*/               x=d%x                                  /*divide the pre─calculated value.*/               end   /*while*/                        /* [↑]  process subsequent args.  */     return x                                         /*return with the LCM of the args.*/

output   when using the (internal) supplied list:

the LCM of      19  and   0                   is ───►   0
the LCM of       0  and  85                   is ───►   0
the LCM of      14  and  -6                   is ───►   42
the LCM of      18  and  12                   is ───►   36
the LCM of      18  and  12  and  -5          is ───►   180
the LCM of      18  and  12  and  -5  and  97 is ───►   17460
the LCM of 2**19-1  and  2**521-1             is ───►   3599124170836896975638715824247986405702540425206233163175195063626010878994006898599180426323472024265381751210505324617708575722407440034562999570663839968526337


### version 2

Translation of: REXX version 0
using different argument handling-

Use as lcm(a,b,c,---)

lcm2: procedurex=abs(arg(1))do k=2 to arg() While x<>0  y=abs(arg(k))  x=x*y/gcd2(x,y)  endreturn x gcd2: procedurex=abs(arg(1))do j=2 to arg()  y=abs(arg(j))  If y<>0 Then Do    do until z==0      z=x//y      x=y      y=z      end    end  endreturn x

## Ring

 see lcm(24,36) func lcm m,n     lcm = m*n / gcd(m,n)     return lcm func gcd gcd, b     while b           c   = gcd           gcd = b           b   = c % b     end     return gcd

## Ruby

Ruby has an Integer#lcm method, which finds the least common multiple of two integers.

irb(main):001:0> 12.lcm 18=> 36

I can also write my own lcm method. This one takes any number of arguments.

def gcd(m, n)  m, n = n, m % n until n.zero?  m.absend def lcm(*args)  args.inject(1) do |m, n|    return 0 if n.zero?    (m * n).abs / gcd(m, n)  endend p lcm 12, 18, 22p lcm 15, 14, -6, 10, 21
Output:
396
210


## Run BASIC

print lcm(22,44) function lcm(m,n) while n   t = m   m = n   n = t mod n wendlcm = mend function

## Rust

This implementation uses a recursive implementation of Stein's algorithm to calculate the gcd.

use std::cmp::{max, min}; fn gcd(a: usize, b: usize) -> usize {    match ((a, b), (a & 1, b & 1)) {        ((x, y), _) if x == y => y,        ((0, x), _) | ((x, 0), _) => x,        ((x, y), (0, 1)) | ((y, x), (1, 0)) => gcd(x >> 1, y),        ((x, y), (0, 0)) => gcd(x >> 1, y >> 1) << 1,        ((x, y), (1, 1)) => {            let (x, y) = (min(x, y), max(x, y));            gcd((y - x) >> 1, x)        }        _ => unreachable!(),    }} fn lcm(a: usize, b: usize) -> usize {    a * b / gcd(a, b)} fn main() {    println!("{}", lcm(6324, 234))}

## Scala

def gcd(a: Int, b: Int):Int=if (b==0) a.abs else gcd(b, a%b)def lcm(a: Int, b: Int)=(a*b).abs/gcd(a,b)
lcm(12, 18)   // 36lcm( 2,  0)   // 0lcm(-6, 14)   // 42

## Scheme

> (lcm 108 8)216

$include "seed7_05.s7i"; const func integer: gcd (in var integer: a, in var integer: b) is func result var integer: gcd is 0; local var integer: help is 0; begin while a <> 0 do help := b rem a; b := a; a := help; end while; gcd := b; end func; const func integer: lcm (in integer: a, in integer: b) is return a div gcd(a, b) * b; const proc: main is func begin writeln("lcm(35, 21) = " <& lcm(21, 35)); end func; Original source: [1] ## Sidef Built-in: say Math.lcm(1001, 221) Using GCD: func gcd(a, b) { while (a) { (a, b) = (b % a, a) } return b} func lcm(a, b) { (a && b) ? (a / gcd(a, b) * b) : 0} say lcm(1001, 221) Output: 17017  ## Smalltalk Smalltalk has a built-in lcm method on SmallInteger: 12 lcm: 18 ## Sparkling function factors(n) { var f = {}; for var i = 2; n > 1; i++ { while n % i == 0 { n /= i; f[i] = f[i] != nil ? f[i] + 1 : 1; } } return f;} function GCD(n, k) { let f1 = factors(n); let f2 = factors(k); let fs = map(f1, function(factor, multiplicity) { let m = f2[factor]; return m == nil ? 0 : min(m, multiplicity); }); let rfs = {}; foreach(fs, function(k, v) { rfs[sizeof rfs] = pow(k, v); }); return reduce(rfs, 1, function(x, y) { return x * y; });} function LCM(n, k) { return n * k / GCD(n, k);} ## Swift Using the Swift GCD function. func lcm(a:Int, b:Int) -> Int { return abs(a * b) / gcd_rec(a, b)} ## Tcl proc lcm {p q} { set m [expr {$p * $q}] if {!$m} {return 0}    while 1 {	set p [expr {$p %$q}]	if {!$p} {return [expr {$m / $q}]} set q [expr {$q % $p}] if {!$q} {return [expr {$m /$p}]}    }}

Demonstration

puts [lcm 12 18]

Output:

36


## TI-83 BASIC

lcm(12,18               36

## TSE SAL

// library: math: get: least: common: multiple <description></description> <version control></version control> <version>1.0.0.0.2</version> <version control></version control> (filenamemacro=getmacmu.s) [<Program>] [<Research>] [kn, ri, su, 20-01-2013 14:36:11]INTEGER PROC FNMathGetLeastCommonMultipleI( INTEGER x1I, INTEGER x2I ) // RETURN( x1I * x2I / FNMathGetGreatestCommonDivisorI( x1I, x2I ) ) //END // library: math: get: greatest: common: divisor <description>greatest common divisor whole numbers. Euclid's algorithm. Recursive version</description> <version control></version control> <version>1.0.0.0.3</version> <version control></version control> (filenamemacro=getmacdi.s) [<Program>] [<Research>] [kn, ri, su, 20-01-2013 14:22:41]INTEGER PROC FNMathGetGreatestCommonDivisorI( INTEGER x1I, INTEGER x2I ) // IF ( x2I == 0 )  //  RETURN( x1I )  // ENDIF // RETURN( FNMathGetGreatestCommonDivisorI( x2I, x1I MOD x2I ) ) //END PROC Main() // STRING s1[255] = "10" STRING s2[255] = "20" REPEAT  IF ( NOT ( Ask( "math: get: least: common: multiple: x1I = ", s1, _EDIT_HISTORY_ ) ) AND ( Length( s1 ) > 0 ) ) RETURN() ENDIF  IF ( NOT ( Ask( "math: get: least: common: multiple: x2I = ", s2, _EDIT_HISTORY_ ) ) AND ( Length( s2 ) > 0 ) ) RETURN() ENDIF  Warn( FNMathGetLeastCommonMultipleI( Val( s1 ), Val( s2 ) ) ) // gives e.g. 10 UNTIL FALSEEND

$txr -p '(lcm (expt 2 123) (expt 6 49) 17)'43259338018880832376582582128138484281161556655442781051813888 ## uBasic/4tH Translation of: BBC BASIC Print "LCM of 12 : 18 = "; FUNC(_LCM(12,18)) End _GCD_Iterative_Euclid Param(2) Local (1) Do While [email protected] [email protected] = [email protected] [email protected] = [email protected] [email protected] = [email protected] % [email protected] LoopReturn (ABS([email protected])) _LCM Param(2)If [email protected]*[email protected] Return (ABS([email protected]*[email protected])/FUNC(_GCD_Iterative_Euclid([email protected],[email protected])))Else Return (0)EndIf Output: LCM of 12 : 18 = 36 0 OK, 0:330 ## UNIX Shell ${\displaystyle \operatorname {lcm} (m,n)=\left|{\frac {m\times n}{\operatorname {gcd} (m,n)}}\right|}$ Works with: Bourne Shell gcd() { # Calculate$1 % $2 until$2 becomes zero.	until test 0 -eq "$2"; do # Parallel assignment: set -- 1 2 set -- "$2" "expr "$1" % "$2""	done 	# Echo absolute value of $1. test 0 -gt "$1" && set -- "expr 0 - "$1"" echo "$1"} lcm() {	set -- "$1" "$2" "gcd "$1" "$2""	set -- "expr "$1" \* "$2" / "$3"" test 0 -gt "$1" && set -- "expr 0 - "$1"" echo "$1"} lcm 30 -42# => 210

### C Shell

alias gcd eval \''set gcd_args=( \!*:q )	\\	@ gcd_u=$gcd_args[2] \\ @ gcd_v=$gcd_args[3]			\\	while ( $gcd_v != 0 ) \\ @ gcd_t =$gcd_u % $gcd_v \\ @ gcd_u =$gcd_v		\\		@ gcd_v = $gcd_t \\ end \\ if ($gcd_u < 0 ) @ gcd_u = - $gcd_u \\ @$gcd_args[1]=$gcd_u \\'\' alias lcm eval \''set lcm_args=( \!*:q ) \\ @ lcm_m =$lcm_args[2]			\\	@ lcm_n = $lcm_args[3] \\ gcd lcm_d$lcm_m $lcm_n \\ @ lcm_r = ($lcm_m * $lcm_n ) /$lcm_d	\\	if ( $lcm_r < 0 ) @ lcm_r = -$lcm_r	\\	@ $lcm_args[1] =$lcm_r			\\'\' lcm result 30 -42echo \$result# => 210

## Ursa

import "math"out (lcm 12 18) endl console
Output:
36

## Vala

 int lcm(int a, int b){    /*Return least common multiple of two ints*/    // check for 0's                                                                if (a == 0 || b == 0)	return 0;     // Math.abs(x) only works for doubles, Math.absf(x) for floats                  if (a < 0)        a *= -1;    if (b < 0)	b *= -1;     int x = 1;    while (true){        if (a * x % b == 0)            return a*x;        x++;    }} void main(){    int	a = 12;    int	b = 18;     stdout.printf("lcm(%d, %d) = %d\n",	a, b, lcm(a, b));}

## VBScript

Function LCM(a,b)	LCM = POS((a * b)/GCD(a,b))End Function Function GCD(a,b)	Do		If a Mod b > 0 Then			c = a Mod b			a = b			b = c		Else			GCD = b			Exit Do		End If	LoopEnd Function Function POS(n)	If n < 0 Then		POS = n * -1	Else		POS = n	End IfEnd Function i = WScript.Arguments(0)j = WScript.Arguments(1) WScript.StdOut.Write "The LCM of " & i & " and " & j & " is " & LCM(i,j) & "."WScript.StdOut.WriteLine
Output:
C:\>cscript /nologo lcm.vbs 12 18
The LCM of 12 and 18 is 36.

C:\>cscript /nologo lcm.vbs 14 -6
The LCM of 14 and -6 is 42.

C:\>cscript /nologo lcm.vbs 0 35
The LCM of 0 and 35 is 0.

C:\>

## Wortel

Operator

@lcm a b

Number expression

!#~km a b

Function (using gcd)

&[a b] *b /a @gcd a b

## XPL0

include c:\cxpl\codes; func GCD(M,N);  \Return the greatest common divisor of M and Nint  M, N;int  T;[while N do     \Euclid's method    [T:= M;  M:= N;  N:= rem(T/N)];return M;]; func LCM(M,N);  \Return least common multipleint  M, N;return abs(M*N) / GCD(M,N); \Display the LCM of two integers entered on command lineIntOut(0, LCM(IntIn(8), IntIn(8)))

## Yabasic

sub gcd(u, v)    local t     u = int(abs(u))    v = int(abs(v))    while(v)        t = u        u = v        v = mod(t, v)    wend    return uend sub sub lcm(m, n)    return m / gcd(m, n) * nend sub print "Least common multiple: ", lcm(12345, 23044)

## zkl

fcn lcm(m,n){ (m*n).abs()/m.gcd(n) }  // gcd is a number method
Output:
zkl: lcm(12,18)
36
zkl: lcm(-6,14)
42
zkl: lcm(35,0)
0