IL-GILLIS 2015 Problem 4

Let $k,m,n$ be positive integers such that $n^m$ is divisible by $m^n$ , and $m^k$ is divisible by $k^m$ . [list=a] [] Prove that $n^k$ is divisible by $k^n$ . [] Find an example of $k,m,n$ satisfying the above conditions, where all three numbers are distinct and bigger than 1. [/list]