I'm not going to list the choices here, mainly because I just want the general idea. If I generalize the question and was given $n$ different integers divide some integer $r$, how do I determine what else it is divisible by?
My initial attempt at the problem was that it should be divisible by $2$ (since $8$ is divisible by $2$), and $3$ and $5$ (since $15$ is divisible by those). Then I thought the number should be divisible by $2, 3,$ and $5$. But apparently that's incorrect.