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:

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)