1. The problem statement, all variables and given/known data Let m and n be relatively prime positive integers. Show that if there are, up to isomorphism, r abelian groups of order m and s of order n, then there are rs abelian groups of order mn. 2. Relevant equations 3. The attempt at a solution I'm not sure how to go about this. I was thinking of saying that since m and n are relatively prime, the gcd(m,n)=1; wouldn't this then imply that the group order would be mn? Because mn is the lcm of m and n? Any help is appreciated.