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What is the smallest positive integer n such that 2n is a perfect square and 3n is a perfect cube and 5n is a perfect fifth power?

 Jan 8, 2022
 #1
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2^15 * 3^20 * 5^24
 

When doubled, each prime factor has an even exponent, making it a square. When tripled each prime factor has an exponent divisible by 3, making it a cube. And when multiplied by 5 each prime factor has an exponent divisible by 5 making it a power of 5.

 Jan 9, 2022
 #2
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nice job guest!

 Jan 9, 2022

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