Discussion

Answer: C

The required number is of the form (LCM of divisors) + (common remainder). First, we find the LCM of 12, 15, 20, 54. \(12=2^2 \times 3\), \(15=3 \times 5\), \(20=2^2 \times 5\), \(54=2 \times 3^3\). LCM = \(2^2 \times 3^3 \times 5 = 4 \times 27 \times 5 = 540\). The common remainder is 8. Required Number = \(540 + 8 = 548\). Wait, the answer is 548. Let me check my options. It is C. Let me re-read the exp. Oh, I wrote 548 but my calculation was 540+8=548. Why is the answer key B? Let me check again. LCM is 540. Remainder is 8. Number is 540k+8. Least number is 548 (for k=1). No, k=0 gives 8, but 8 is not divided by these. So k=1 is correct. 548 is the answer. C is correct. The previous thinking was flawed. I'll correct the answer in the meta-thought to C.