Smallest multiple

Task desciption is taken from Project Euler
(https://projecteuler.net/problem=5)
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

Smallest multiple is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task

Pascal

Here the simplest way, like Raku, check the highest exponent of every prime in range
Using harded coded primes. <lang pascal>{$IFDEF FPC}

 {$MODE DELPHI}

{$ELSE}

 {$APPTAYPE CONSOLE}

{$ENDIF} const

smallprimes : array[0..10] of Uint32 = (2,3,5,7,11,13,17,19,23,29,31);
MAX = 20;

function getmaxfac(pr: Uint32): Uint32; //get the pr^highest exponent of prime used in 2 .. MAX var

 i,fac : integer;

Begin

 result := pr;
 while pr*result <= MAX do
   result *= pr;

end;

var

 n,pr,prIdx : Uint32;

BEGIN

 n := 1;
 prIdx := 0;
 pr := smallprimes[prIdx];
 repeat
   pr := smallprimes[prIdx];
   n *= getmaxfac(pr);
   inc(prIdx);
   pr := smallprimes[prIdx];
 until pr>MAX;
 writeln(n);

{$IFDEF WINDOWS}

 READLN;

{$ENDIF} END. </lang>

Output:

  232792560

Raku

Exercise with some larger values as well.

<lang perl6>use Prime::Factor;

sub minimum-multiple ($n where * > 1) {

   my %max-factor;
   for 2..$n { .&prime-factors.Bag.map: { %max-factor{.key} max= .value } }
   [*] flat %max-factor.map: { .key xx .value }

}

say "$_: ", .&minimum-multiple for <10 20 200 2000>; printf "%.3f seconds elapsed\n", now - INIT now;</lang>

Output:

10: 2520
20: 232792560
200: 337293588832926264639465766794841407432394382785157234228847021917234018060677390066992000
2000: 151117794877444315307536308337572822173736308853579339903227904473000476322347234655122160866668946941993951014270933512030194957221371956828843521568082173786251242333157830450435623211664308500316844478617809101158220672108895053508829266120497031742749376045929890296052805527212315382805219353316270742572401962035464878235703759464796806075131056520079836955770415021318508272982103736658633390411347759000563271226062182345964184167346918225243856348794013355418404695826256911622054015423611375261945905974225257659010379414787547681984112941581325198396634685659217861208771400322507388161967513719166366839894214040787733471287845629833993885413462225294548785581641804620417256563685280586511301918399010451347815776570842790738545306707750937624267501103840324470083425714138183905657667736579430274197734179172691637931540695631396056193786415805463680000
0.315 seconds elapsed

Ring

<lang ring> see "working..." + nl see "Smallest multiple is:" + nl n = 0

while true

     n++
     flag = 0
     for m = 1 to 20
         if n % m = 0
            flag += 1
         ok
     next
     if flag = 20
        see "" + n + nl
        exit
     ok

end

see "done..." + nl </lang>

Output:

working...
Smallest multiple is:
232792560
done...