Multiple choice

Find the greatest number of five digits which when divided by 3, 5, 8, 12 have 2 as remainder.

  1. 99999

  2. 99958

  3. 99960

  4. 99962
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The greatest 5-digit number is 99999. We need a number that leaves remainder 2 when divided by 3, 5, 8, and 12. This means N-2 must be divisible by the LCM of 3, 5, 8, 12. LCM(3,5,8,12) = 120. The largest multiple of 120 less than 99999 is 99960. Adding 2 gives 99962. Checking: 99962 ÷ 3 = 33320 remainder 2, 99962 ÷ 5 = 19992 remainder 2, etc. Option C (99960) would leave remainder 0, not 2.

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