Prove or disprove statements about the greatest common divisor Help with prove or disproving either of these statements would be really appreciated, one or the other is fine, I just need a start or a solution to one and I'm sure I could probably figure the other out.

(a) For all $a, b, c \in \mathbb{Z}$, $\gcd(ac, bc) = c \gcd(a, b)$
(b) For all $a, b, c \in \mathbb{Z}$, $\gcd(ab, c) = \gcd(a, b) \gcd(b, c)$


Hint for (a): Note that $c|ac$ and $c|bc$.
Hint for (b): Look at special cases, $a=b$, $a=c$ etc
