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:

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)