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?
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.