Huff Norris
06/05/2024 · Junior High School
What is the least common multiple (LCM) of 4 and 6?
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Step-by-step Solution
To find the least common multiple (LCM) of 4 and 6, we can use the prime factorization method.
1. **Prime factorization**:
- The prime factorization of 4 is \(2^2\).
- The prime factorization of 6 is \(2^1 \times 3^1\).
2. **Identify the highest power of each prime**:
- For the prime number 2, the highest power in the factorizations is \(2^2\) (from 4).
- For the prime number 3, the highest power is \(3^1\) (from 6).
3. **Multiply these together**:
\[
\text{LCM} = 2^2 \times 3^1 = 4 \times 3 = 12
\]
Thus, the least common multiple of 4 and 6 is \( \boxed{12} \).
Quick Answer
The LCM of 4 and 6 is 12.
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