Let a,b,c be integers such that a and c are coprime, and b and c are coprime. Prove that ab and c are coprime.

I am stuck with this, I can see that gcd(a,b,c) = gcd(a,gcd(b,c)) = gcd (a,1)= 1 so a,b and c are all pairwise coprime, but how do I show ab and c are coprime?