C++ algorithm to calculate least common multiple for multiple numbers

Question

Is there a C++ algorithm to calculate the least common multiple for multiple numbers, like lcm(3,6,12) or lcm(5,7,9,12)?

Answer 1

The algorithm isn't specific to C++. AFAIK, there's no standard library function.

To calculate the LCM, you first calculate the GCD (Greatest Common Divisor) using Euclids algorithm.

http://en.wikipedia.org/wiki/Greatest_common_divisor

The GCD algorithm is normally given for two parameters, but...

GCD (a, b, c) = GCD (a, GCD (b, c))
              = GCD (b, GCD (a, c))
              = GCD (c, GCD (a, b))
              = ...

To calculate the LCM, use...

                a * b
LCM (a, b) = ----------
             GCD (a, b)

The logic for that is based on prime factorization. The more general form (more than two variables) is...

                                          a                 b        
LCM (a, b, ...) = GCD (a, b, ...) * --------------- * --------------- * ...
                                    GCD (a, b, ...)   GCD (a, b, ...)

EDIT - actually, I think that last bit may be wrong. The first LCM (for two parameters) is right, though.