elementary number theory - Prove that if $gcd(a,b)=1$, then $gcd(acdot b,c) = gcd(a,c)cdot gcd(b,c)$.

Let $a,b,c \in \mathbb{Z}$, prove that if $\gcd(a,b)=1$, then $\gcd(a\cdot b,c) = \gcd(a,c)\cdot \gcd(b,c)$.