Find the least common multiple.

Question

9 and 15

Answer 1

To find the least common multiple (LCM) of 9 and 15, we can use the prime factorization method.

1. First, we find the prime factorization of each number:

   • The prime factorization of 9 is \(3^2\).
   • The prime factorization of 15 is \(3^1 \times 5^1\).

2. Next, we take the highest power of each prime factor that appears in these factorizations:

   • For the prime number 3, the highest power is \(3^2\) (from 9).
   • For the prime number 5, the highest power is \(5^1\) (from 15).

3. Now, we multiply these highest powers together to find the LCM: \[ LCM = 3^2 \times 5^1 = 9 \times 5 = 45 \]

Thus, the least common multiple of 9 and 15 is 45.