Question
The least common multiple of two numbers is 24. Which could be the two numbers?
6 and 8
4 and 6
8 and 16
4 and 12
6 and 8
4 and 6
8 and 16
4 and 12
Answers
GPT-4o mini
To find which pair of numbers has a least common multiple (LCM) of 24, we can calculate the LCM for each pair:
1. **6 and 8**:
- Prime factorization:
- 6 = 2 × 3
- 8 = 2^3
- LCM = max(2^3, 3) = 2^3 × 3 = 24
2. **4 and 6**:
- Prime factorization:
- 4 = 2^2
- 6 = 2 × 3
- LCM = max(2^2, 3) = 2^2 × 3 = 12
3. **8 and 16**:
- Prime factorization:
- 8 = 2^3
- 16 = 2^4
- LCM = max(2^3, 2^4) = 2^4 = 16
4. **4 and 12**:
- Prime factorization:
- 4 = 2^2
- 12 = 2^2 × 3
- LCM = max(2^2, 3) = 2^2 × 3 = 12
From this calculation, the only pair whose LCM is 24 is **6 and 8**. Thus, the correct answer is:
**6 and 8**
1. **6 and 8**:
- Prime factorization:
- 6 = 2 × 3
- 8 = 2^3
- LCM = max(2^3, 3) = 2^3 × 3 = 24
2. **4 and 6**:
- Prime factorization:
- 4 = 2^2
- 6 = 2 × 3
- LCM = max(2^2, 3) = 2^2 × 3 = 12
3. **8 and 16**:
- Prime factorization:
- 8 = 2^3
- 16 = 2^4
- LCM = max(2^3, 2^4) = 2^4 = 16
4. **4 and 12**:
- Prime factorization:
- 4 = 2^2
- 12 = 2^2 × 3
- LCM = max(2^2, 3) = 2^2 × 3 = 12
From this calculation, the only pair whose LCM is 24 is **6 and 8**. Thus, the correct answer is:
**6 and 8**