Multiple choice

What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?

  1. 1012

  2. 1022

  3. 1122

  4. 1222
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B Correct answer
Explanation

LCM of 3, 4, 5, 6 is 60. Multiples of 60: 60, 120, ..., 960, 1020. The smallest 4-digit multiple is 1020. Adding the remainder 2 gives 1022.

AI explanation

Find the least common multiple of 3, 4, 5 and 6, which is 60. Since all divisors leave a remainder of 2, the required number takes the form 60k plus 2. The smallest four-digit number occurs when k is 17, giving 1020 plus 2. The least four-digit number satisfying the condition is 1022.

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