I have this math question that I'm kind of confused on. This is the question:
Let $A, B, C$ and $D$ be integers with $A \mid C$ and $B \mid D$ show that $$ AB \mid CD. $$
I'm not 100% sure as to how to start this problem. This is what I did so far. I can rewrite $A | C$ as $C = A \cdot K$ for some $k\in \mathbb{Z}$ and $B | D$ as $D = B\cdot J$ for some $J\in \mathbb{Z}$. I now know that $CD=(A\cdot K)\cdot (B\cdot J)=(AB)(KJ)$. I'm not sure how to finish this problem. Thanks.