HMMT November 2017 T1

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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.

Dataset text NuminaMath olympiads. Quoted with source.

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1024

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