Multiple choice

What least number must be subtracted from 1294 so that the result when divided by 9, 11, and 13 will leave 6 as remainder in each case?

  1. 1

  2. 3

  3. 5

  4. 7
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A Correct answer
Explanation

Find the LCM of 9, 11, and 13, which is 1287. To leave a remainder of 6, the number must be of the form 1287k + 6. For k=1, the number is 1293. Subtracting 1293 from 1294 gives 1.

AI explanation

The least common multiple of 9, 11 and 13 is 1287. To leave a remainder of 6, the required target number is 1287 + 6 = 1293. Therefore, the number to be subtracted from 1294 is 1294 - 1293 = 1. The result is 1.

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