Asked by Brianna sapp
What is the least common multiple (LCM) of the numbers 6 and 8?
Responses
A 1818
B 2424
C 2727
D 3232
Responses
A 1818
B 2424
C 2727
D 3232
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the least common multiple (LCM) of 6 and 8, we can use the prime factorization method.
1. **Prime Factorization**:
- The prime factorization of 6 is \(2^1 \times 3^1\).
- The prime factorization of 8 is \(2^3\).
2. **Identify the highest power of each prime**:
- For the prime number 2, the highest power is \(2^3\).
- For the prime number 3, the highest power is \(3^1\).
3. **Multiply these together to find the LCM**:
\[
\text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24
\]
Thus, the least common multiple of 6 and 8 is 24.
None of the answer choices provided (A: 1818, B: 2424, C: 2727, D: 3232) are correct. The correct answer is 24, which does not appear among the options.
1. **Prime Factorization**:
- The prime factorization of 6 is \(2^1 \times 3^1\).
- The prime factorization of 8 is \(2^3\).
2. **Identify the highest power of each prime**:
- For the prime number 2, the highest power is \(2^3\).
- For the prime number 3, the highest power is \(3^1\).
3. **Multiply these together to find the LCM**:
\[
\text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24
\]
Thus, the least common multiple of 6 and 8 is 24.
None of the answer choices provided (A: 1818, B: 2424, C: 2727, D: 3232) are correct. The correct answer is 24, which does not appear among the options.
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