Problem Statement

Compute the   least common multiple   (LCM)   of two integers. Given   m   and   n,   the least common multiple is the smallest positive integer that has both   m   and   n   as factors.

The least common multiple of   12   and   18   is   36,       because:

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.

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

Let's start with the solution:

Textwindow.Write("LCM(35, 21) = ")
mlcm = 35
nlcm = 21
CalculateLCM()
TextWindow.WriteLine(lcm)

Sub CalculateLCM
  mgcd = mlcm
  ngcd = nlcm 
  CalculateGCD() 
  lcm = mlcm / gcd * nlcm
EndSub 

Sub CalculateGCD
  While mgcd <> 0
    tmp = mgcd
    mgcd = Math.Remainder(ngcd, mgcd)
    ngcd = tmp
  EndWhile
  gcd = ngcd
EndSub