elementary number theory - $gcd(ab,c)$ equals $gcd(a,c)$ times $gcd( b, c)$

Let $a,b,c$ be integers, prove that if $\gcd(a,b) =1$ then
$\gcd(ab,c) = \gcd(a,c)\times\gcd(b,c)$

I don't know what to do after I got the combinations of $ab$ and $c$.