Question
What is the least common multiple (LCM) of 8 and 10?
A.
160
B.
40
C.
2
D.
80
A.
160
B.
40
C.
2
D.
80
Answers
GPT-4o mini
To find the least common multiple (LCM) of 8 and 10, we can use the prime factorization method.
1. **Find the prime factorization**:
- 8 = \(2^3\)
- 10 = \(2^1 \times 5^1\)
2. **Take the highest power of each prime**:
- For the prime number 2: the highest power between \(2^3\) (from 8) and \(2^1\) (from 10) is \(2^3\).
- For the prime number 5: the highest power is \(5^1\) (from 10).
3. **Multiply these together to find the LCM**:
\[
LCM = 2^3 \times 5^1 = 8 \times 5 = 40
\]
Thus, the least common multiple of 8 and 10 is 40.
The correct answer is **B. 40**.
1. **Find the prime factorization**:
- 8 = \(2^3\)
- 10 = \(2^1 \times 5^1\)
2. **Take the highest power of each prime**:
- For the prime number 2: the highest power between \(2^3\) (from 8) and \(2^1\) (from 10) is \(2^3\).
- For the prime number 5: the highest power is \(5^1\) (from 10).
3. **Multiply these together to find the LCM**:
\[
LCM = 2^3 \times 5^1 = 8 \times 5 = 40
\]
Thus, the least common multiple of 8 and 10 is 40.
The correct answer is **B. 40**.