Bob Burgess
01/31/2024 · High School
What is the least common mulriple of 4 , 7 , and 6 ?
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To find the least common multiple (LCM) of the numbers 4, 7, and 6, we can use the prime factorization method.
1. **Prime factorization**:
- \(4 = 2^2\)
- \(7 = 7^1\)
- \(6 = 2^1 \times 3^1\)
2. **Identify the highest power of each prime**:
- The prime factors involved are 2, 3, and 7.
- The highest power of 2 is \(2^2\) (from 4).
- The highest power of 3 is \(3^1\) (from 6).
- The highest power of 7 is \(7^1\) (from 7).
3. **Multiply these together**:
\[
\text{LCM} = 2^2 \times 3^1 \times 7^1 = 4 \times 3 \times 7
\]
4. **Calculate step by step**:
- First, calculate \(4 \times 3 = 12\).
- Then, calculate \(12 \times 7 = 84\).
Thus, the least common multiple of 4, 7, and 6 is **84**.
Quick Answer
The least common multiple of 4, 7, and 6 is 84.
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