Show that if a, b, c, and d are integers such that
a | c and b | d, then ab | cd.
From $\displaystyle a|c$ we get that for some $\displaystyle m \in \mathbb{N}$, c = am. Also, from $\displaystyle b|d$ we get that for some $\displaystyle n \in \mathbb{N}$, d = nb.
Now, what is ab? Can you see how the above facts help us show the desired result?