To find the least common multiple (LCM) of the numbers 9, 15, 18, and 20 using prime factorization, follow these steps:
Step 1: Prime factorize each number.
9: 3^2
15: 3 * 5
18: 2 * 3^2
20: 2^2 * 5
Step 2: Identify the highest power of each prime factor.
The highest power of 2 is 2^2.
The highest power of 3 is 3^2.
The highest power of 5 is 5.
Step 3: Multiply the highest powers of each prime factor together.
2^2 * 3^2 * 5 = 4 * 9 * 5 = 180
Therefore, the LCM of 9, 15, 18, and 20 is 180.