Multiple choice

A number when divided by 3,4,5,6,7,8,9 and 10 leaves a remainder of 2,3,4,5,6,7,8 and 9 respectively. What is the smallest such number?

  1. 2579

  2. 2559

  3. 2539

  4. 2519
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The difference between each divisor and its 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. Thus, 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.

Keep practicing — related questions