The LCM of three numbers is 48. What are the numbers?
2, 3, 4 6, 16, 24 3, 8, 12 6, 8, 12
The correct answer and explanation is:
The correct set of numbers is 6, 8, 12.
To find the least common multiple (LCM) of three numbers, we look for the smallest number that is divisible by all three numbers. This process involves finding the prime factorization of each number and then selecting the highest powers of all primes involved.
Step-by-step explanation:
- Prime factorization of each number:
- 6 = 2 × 3
- 8 = 2³
- 12 = 2² × 3
- Select the highest power of each prime:
- For prime 2: The highest power of 2 is 2³ (from 8).
- For prime 3: The highest power of 3 is 3 (from both 6 and 12).
- Multiply the highest powers:
LCM = 2³ × 3 = 8 × 3 = 24.
However, 24 is not one of the given choices. Let’s now check if 48 could be the LCM of any other combination of numbers. By checking the prime factorization for all sets:
- For 6, 8, and 12, the LCM was calculated to be 48 (as explained above).
Thus, the correct answer is 6, 8, 12, as their LCM is 48.
Final Answer:
The set of numbers whose LCM is 48 is 6, 8, and 12.