Multiple choice

The greatest four digit number which when divided by $18$ and $12$ leaves a remainder of $4$ in each case is?

  1. $9976$
  2. $9940$
  3. $9904$
  4. $9868$
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A Correct answer
Explanation

The LCM of 18 and 12 is 36. The greatest four-digit number is 9999; dividing 9999 by 36 gives a remainder of 27. Subtracting 27 from 9999 gives 9972, which is divisible by 36, and adding the required remainder of 4 results in 9976.

AI explanation

Find the least common multiple of 18 and 12, which is 36. The greatest four-digit number is 9999, and dividing it by 36 gives a remainder of 27. Subtracting this remainder from 9999 gives 9972, so a final remainder of 4 requires adding 4 to this base, making the number 9976.

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