Multiple choice

Find the lowest 4-digit number which when divided by 3 , 4 or 5 leaves a remainder of 2 in each case?

  1. $1022$
  2. $2300$
  3. $3044$
  4. $1111$
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A Correct answer
Explanation

The number must be of the form LCM(3, 4, 5) * k + 2. The LCM is 60. We need the smallest 4-digit number 60k + 2 >= 1000. 60 * 17 = 1020, so 1020 + 2 = 1022.

AI explanation

Calculate the least common multiple of 3, 4, and 5, which is 60. The required number must be of the form 60k plus 2, so we check the lowest values. For k equals 17, the calculation 60 times 17 plus 2 gives 1022, which is the lowest four-digit number satisfying the condition.

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