A while ago, I gave my Pre-algebra class a puzzle problem: "Given two natural numbers, m and n. If their GCD is G=6 and their LCM is L=72, what are the numbers?"

a) What were all possible (m, n) for G=6 and L=72 (m<=n)?

b) What's the smallest sum, m+n, for any (m, n) pair that share the same G=gcd and L=lcm (with another m<=n; G>=2)?

c) Find the (G, L) pair with the most solutions (m, n) for the same G=gcd(m,n) and L=lcm(m,n) (G>1, L < 1001).

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## BMAD 65

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