7:05 AM
Should one of these two questions be closed as a duplicate? Which one should be left open?
5

How do I go about proving this? If gcd (a,b)=1 and gcd (a,c)=1, then gcd (a,bc)=1. I'm very confused with gcd proofs.

4

Show that \$\gcd(a,bc)=1\$ if and only if \$\gcd(a,b)=1\$ and \$\gcd(a,c)=1\$. I am new at proofs and I think I should use Euclid's Lemma which states "If \$p\$ is a prime that divides \$ab\$, then \$p\$ divides \$a\$ or \$p\$ divides \$b\$. However, I am not sure how to create a concrete proof or argument. Any ...

The newer question asks for equivalence, but one direction is, in my opinion, easy.
The older question has more answers.