Find the Least Common Multiple (LCM) of 25 and 15. Show Your Work

1 answer

To find the LCM of 25 and 15, we first need to find the prime factorization of each number.

25 = 5 * 5
15 = 3 * 5

Next, we identify the highest power of each prime factor that appears in either number:

Prime factor 3 appears in 15 (3^1) and not in 25
Prime factor 5 appears in both numbers as 5^2 in 25 and 5^1 in 15

To find the LCM, we multiply the highest power of each prime factor:

LCM = 3^1 * 5^2
LCM = 3 * 25
LCM = 75

Therefore, the LCM of 25 and 15 is 75.