If gcd(m,n)=1 and gcd(k,n)=1, show that gcd(mk,n)=1.

I have tried approaching it by doing a proof of the contrapositive, but I keep getting stuck..

Let m,k,n be integers such that gcd(mk,n)\neq{1}. Then there exists d>1 such that d=gcd(mk,n). Then, d divides mk and d divides n. So, d divides (mk+n) etc....

any advice on where to go from here?? thanks!!!