Multiple choice

What will be the least number which when divided by 12, 21 and 35 leaves 6 as a remainder in each case?

  1. 426

  2. 326

  3. 536

  4. 436
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A Correct answer
AI explanation

The least common multiple (LCM) of 12, 21 and 35 is found by prime factorizing each number: 12 is 2 times 2 times 3, 21 is 3 times 7 and 35 is 5 times 7. The LCM is the product of the highest powers of all prime factors present, which is 4 times 3 times 5 times 7, giving 420. Since the required number leaves a remainder of 6 in each case, we add 6 to the LCM. The least number is 420 plus 6, which is 426.

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