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:

#include 

#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