Correct Answer:
B. 189
This question requires finding the Least Common Multiple (LCM) of two numbers, 27 and 63. The LCM is the smallest positive integer that is divisible by both numbers. One common method is to use prime factorization.
- Prime factorization of 27: 3 x 3 x 3 = 33
- Prime factorization of 63: 3 x 3 x 7 = 32 x 7
- To find the LCM, take the highest power of all prime factors present in either number. Here, the prime factors are 3 and 7. The highest power of 3 is 33 (from 27), and the highest power of 7 is 71 (from 63).
- Correct Option B: 189 is accurate because LCM = 33 x 7 = 27 x 7 = 189.
- Option A: 100 is incorrect as it's not a multiple of 27 or 63.
- Option C: 81 is a multiple of 27 (27 x 3) but not of 63.
- Option D: 216 is a multiple of 27 (27 x 8) but not of 63.