Question
Find the least common multiple of 8 and 12. Type your answer in the box below
Answers
GPT-4o mini
To find the least common multiple (LCM) of 8 and 12, we can follow a few steps:
1. **Prime Factorization**:
- The prime factorization of 8 is \(2^3\).
- The prime factorization of 12 is \(2^2 \times 3^1\).
2. **Identify the Highest Powers**:
- For the prime number 2, the highest power in both factorizations is \(2^3\).
- For the prime number 3, the highest power is \(3^1\).
3. **Multiply the Highest Powers Together**:
- LCM = \(2^3 \times 3^1 = 8 \times 3 = 24\).
Thus, the least common multiple of 8 and 12 is **24**.
1. **Prime Factorization**:
- The prime factorization of 8 is \(2^3\).
- The prime factorization of 12 is \(2^2 \times 3^1\).
2. **Identify the Highest Powers**:
- For the prime number 2, the highest power in both factorizations is \(2^3\).
- For the prime number 3, the highest power is \(3^1\).
3. **Multiply the Highest Powers Together**:
- LCM = \(2^3 \times 3^1 = 8 \times 3 = 24\).
Thus, the least common multiple of 8 and 12 is **24**.