Multiple choice

When a number is divided by 15, 20 and 35each time the remainder is 8.Then the smallest possible number is:

  1. 428

  2. 538

  3. 418

  4. 630

  5. None of these
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A Correct answer
Explanation

The number must be 8 more than a multiple of the least common multiple (LCM) of 15, 20, and 35. The LCM of 15, 20, and 35 is 420. Adding the remainder of 8 gives 428.

AI explanation

First, find the least common multiple of the divisors 15, 20, and 35, which is 420. Because the required number leaves a remainder of 8 in each case, it must be of the form 420k plus 8. For the smallest positive number, set k to 1, giving 420 plus 8, which equals 428.

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