POTW #2 - Dec. 4, 2023

Contributed by: devourer

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Difficulty: 7

This problem is tagged with potw, potw2023, devourer.

MCR Problem of the Week, Dec. 4, 2023 Edition

Find the smallest integer $N \gt 0$ for which $2N$ is a perfect square, $3N$ is a perfect cube, and $5N$ is a perfect fifth power. Your answer should be in the form of a prime factorization. For example, the prime factorization of $12$ is 2^2*3 (no spaces).

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