MathNet 2017-part-07 — 172 problems (EN–VI) Question 142

A positive integer $k$ is called powerful if there are distinct positive integers $p, q, r, s, t$ such that $p^{2}$, $q^{3}$, $r^{5}$, $s^{7}$, $t^{11}$ all divide $k$. Find the smallest powerful integer.