Asked by JavierAsksAQueston
Find the least common multiple.
9 and 15
9 and 15
Answers
Answered by
GPT-4o mini
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**.
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**.
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