Multiple choice

What is the least number which when divided by 12, 16 and 18 leaves 5 as remainder in each case?

  1. 149

  2. 293

  3. 337

  4. 481
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A Correct answer
Explanation

Find LCM of 12, 16, 18. 12 = 2^2 * 3, 16 = 2^4, 18 = 2 * 3^2. LCM = 2^4 * 3^2 = 16 * 9 = 144. Number = LCM + remainder = 144 + 5 = 149.

AI explanation

Calculate the least common multiple of 12, 16 and 18, which is 144. Because the required remainder in each case is 5, the general form of the number is 144k plus 5. Using k equal to 1 gives the smallest positive value of 144 plus 5. The least number satisfying the given conditions is 149.

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