For positive integers prove that $a\Big|bc \implies a\Big|b \lor a\Big|c$

Question

$a\Big | b,\; b = ak.$ $a\Big|c, c = al,$

So do I multiply $b$ and $c$ to get $a(kl)$ to prove that $bc = a$ multiplied by some integer $kl$ closed under multiplication?

Answer 1

$6 \mid 2\cdot 3, 6 \not \mid 2, 6 \not \mid 3 $.