Question

# Find the smallest possible integer m such that 60m is a square number.

Answer

15

- Q: What are the factors of 60? A: The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
- Q: What are the prime factors of 60? A: The prime factors of 60 are 2, 2, 3, 5.
- Q: What is the highest power of each prime factor that divides 60? A: 2^2 * 3^1 * 5^1.
- Q: In order for 60m to be a square number, we need to find the smallest value of m that will cause each prime factor's power to be even. A: m = 3*5 = 15.