Assume gcd(a,b)=1 and gcd (a,c)=1.

True or false? If true, give a proof. If false, give a counterexample.

a) gcd (bc,a)=1

b) gcd (ab,c)=1

I am pretty sure b) is false. We could do (a,b)=(3,5)=1 and (a,c)=(3,5)=1, but (ab,c)=(15,5)=5...

I am not sure about a) though. I think it is true, but do not know how to prove it.