Multiple choice

What is the second smallest number which upon dividing by 3, 5, 7 and 11 leaves a remainder of 2 in each case?

  1. 2310

  2. 2312

  3. 2314

  4. 2316
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For numbers leaving remainder 2 when divided by 3, 5, 7, 11, we need LCM(3,5,7,11) × k + 2. LCM = 1155. Smallest such number = 1155 + 2 = 1157. Second smallest = 1155 × 2 + 2 = 2310 + 2 = 2312. Option B (2312) is correct.

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