Let r, s, and t be integers, and suppose gcd(r,s)=1, r|t, and s|t.

Prove rs|t.

My work so far:

I have attempted to use the definition of gcd and division to solve the problem.

There exist integers a,b,c,d such that ra + sb = 1, rc = t, and sd = t.

I can prove that t = r(rca)+s(brc), and t^2 = rs(cd), but I just can't get to the right answer.

Thank you.