Multiple choice

Find the least number that should be subtracted from 1000 so that the remainder may be exactly divisible by 9, 12 and 18.

  1. 972

  2. 38

  3. 36

  4. 28
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D Correct answer
Explanation

The LCM of 9, 12, and 18 is 36. Dividing 1000 by 36 gives 1000 = 36 * 27 + 28. The remainder is 28, so subtracting 28 from 1000 makes it exactly divisible by 36.

AI explanation

We first find the least common multiple of 9, 12, and 18, which is 36. We then determine the highest multiple of 36 that is less than 1000 by dividing 1000 by 36, which gives a quotient of 27. Multiplying 36 by 27 yields 972. Subtracting this from 1000 gives 1000 minus 972, which equals 28.

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