Weaver Coles
03/18/2024 · High School
Question 20 ( 5 points) The least common multiple of \( 3,4,6 \), and 8 is A) 96. B) 72 . C) 8. D) 24.
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To find the least common multiple (LCM) of the numbers \(3\), \(4\), \(6\), and \(8\), we can use the prime factorization method.
1. **Prime factorization of each number**:
- \(3 = 3^1\)
- \(4 = 2^2\)
- \(6 = 2^1 \times 3^1\)
- \(8 = 2^3\)
2. **Identify the highest power of each prime factor**:
- For the prime \(2\): the highest power is \(2^3\) (from \(8\)).
- For the prime \(3\): the highest power is \(3^1\) (from \(3\) and \(6\)).
3. **Multiply the highest powers together**:
\[
\text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24
\]
Thus, the least common multiple of \(3\), \(4\), \(6\), and \(8\) is \(24\).
The correct answer is:
**D) 24.**
Quick Answer
The LCM of \(3\), \(4\), \(6\), and \(8\) is \(24\).
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