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Answer:

The Approach: What
does it mean for r to be divisible by m and n? It means that all the
primes in m must go into r, and all primes in n must be in r. What if m
and n have primes in common?

For example, if m is divisible by
3^5 and n is divisible by 3^7, what does this mean about r? It means r
must be divisible by 3^7.

The Rule: For each prime p such that p^a \ m (e.g., m is divisible by p^a) and p^b \ n, r must be divisible by p^max(a, b)

The Algorithm: Define q to be 1. for each prime number p less than m and n: find the largest a and b such that p^a \ m and p^b \ n let q = q * p^max(a, b) return q

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