VTRMC 2018 Problem 4

Let $m, n$ be integers such that $n \geq m \geq 1$ . Prove that $\frac{\text{gcd} (m,n)}{n} \binom{n}{m}$ is an integer. Here $\text{gcd}$ denotes greatest common divisor and $\binom{n}{m} = \frac{n!}{m!(n-m)!}$ denotes the binomial coefficient.