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