Multiple choice

A natural number, when divided by 3, 4, 5, 6, 7, 8, 9 & 10 leaves remainders 2, 3, 4, 5, 6, 7, 8 & 9 respectively. What is the smallest such number?

  1. 2579

  2. 2559

  3. 2539

  4. 2519
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D Correct answer
Explanation

The difference between divisor and remainder is constant (3-2=1, 4-3=1, ..., 10-9=1). The number is LCM(3, 4, 5, 6, 7, 8, 9, 10) - 1. LCM(3, 4, 5, 6, 7, 8, 9, 10) = 2520. 2520 - 1 = 2519.

AI explanation

Notice the pattern that the difference between each divisor and its remainder is 1. Therefore, the required number is 1 less than the least common multiple (LCM) of 3, 4, 5, 6, 7, 8, 9 and 10. The LCM of these divisors is 2520, so subtracting 1 gives the smallest such number as 2519.

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