Prove $n \choose m$ is divisible by n when $\gcd(m,n)=1$

Question

I know that $p \choose k$ is divisible by $p$ for all $k \in \{1, 2, \ldots,p-1\}$. But I am trying to work on a generalization as in the title but do not know how to prove it.

Answer 1

Hint: Consider the fact that $\binom{n-1}{m-1}$ is an integer, and $\binom nm$ is $\frac nm$ times larger.