Multiple choice

Find the greatest 3 digit number such that when they divided by 12, 18, 21 and 28, it leaves a remainder 3 in each case.

  1. 759

  2. 859

  3. 659

  4. 827
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We need a number that leaves remainder 3 when divided by 12, 18, 21, 28. So (N-3) must be divisible by LCM(12,18,21,28). LCM(12,18,21,28) = LCM(2²×3, 2×3², 3×7, 2²×7) = 2²×3²×7 = 4×9×7 = 252. So N-3 = 252k, N = 252k + 3. For greatest 3-digit number: 252×3 + 3 = 756 + 3 = 759. 252×4 + 3 = 1011 (4 digits). So answer is 759.

Keep practicing — related questions