Multiple choice

Find the four digit largest number which when divided by 60, 18 and 20 leaves remainder 3 in each case.

  1. 8970

  2. 9960

  3. 9864

  4. 9903
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Find LCM of 60, 18, 20. 60 = 2² × 3 × 5. 18 = 2 × 3². 20 = 2² × 5. LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180. So the number N = 180k + 3. For the largest 4-digit number: 180k + 3 ≤ 9999. 180k ≤ 9996. k ≤ 55.5, so k = 55. N = 180 × 55 + 3 = 9900 + 3 = 9903. This is a 4-digit number that leaves remainder 3 when divided by 60, 18, and 20. Let's verify: 9903 ÷ 60 = 165 remainder 3. 9903 ÷ 18 = 550 remainder 3. 9903 ÷ 20 = 495 remainder 3. The answer is indeed 9903.

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