Multiple choice

What is the largest three-digit number that leaves a remainder of 1 when divided by 2, 3, 4, 6, and 8?

  1. 976

  2. 984

  3. 985

  4. 992

  5. 997
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C Correct answer
Explanation

The number must be 1 more than a multiple of the LCM of 2, 3, 4, 6, and 8. The LCM is 24. We look for the largest 3-digit multiple of 24, which is 984 (24 * 41). Adding 1 gives 985.

AI explanation

To leave a remainder of 1 when divided by 2, 3, 4, 6, and 8, the number must be exactly 1 more than a common multiple of those divisors. The least common multiple of 2, 3, 4, 6, and 8 is 24. To find the largest three-digit number of this form, we divide 999 by 24 to get a quotient of 41, meaning the largest multiple is 41 * 24 = 984. Adding 1 gives the final number, 985.

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