Multiple choice

What is the smallest 3-digit number which divided by 3, 4, 5 and 6 leaves the remainders 2, 3, 4 and 5 respectively?

  1. 108

  2. 110

  3. 119

  4. 99

  5. 105
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C Correct answer
Explanation

Divisors: 3, 4, 5, 6. Remainders: 2, 3, 4, 5. The difference between divisor and remainder is constant (1). LCM(3, 4, 5, 6) = 60. The number is of the form 60k - 1. For 3-digit, k=2 gives 119.

AI explanation

Notice that the difference between each divisor and its corresponding remainder is exactly 1. Therefore, the required number must be one less than a common multiple of 3, 4, 5, and 6. The least common multiple of 3, 4, 5, and 6 is 60, making the general form of the number 60k minus 1. To find the smallest 3-digit number, let k be 2, which gives 120 minus 1, resulting in 119.

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