Multiple choice

The greatest 4-digit number which when divided by $20, 24$ and $45$ leaves a remainder of $11$ in each case is

  1. $9999$
  2. $9998$
  3. $9997$
  4. $9731$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Find LCM of 20, 24, 45. 20 = 2^2 * 5, 24 = 2^3 * 3, 45 = 3^2 * 5. LCM = 2^3 * 3^2 * 5 = 360. Largest 4-digit number is 9999. 9999 / 360 = 27 with remainder 279. 9999 - 279 = 9720. Add remainder 11: 9720 + 11 = 9731.

AI explanation

Determine the least common multiple of 20, 24, and 45. The prime factorizations show the LCM is 2 squared times 2 times 3 times 5 times 3 times 5, which equals 360. The greatest four-digit number is 9999; dividing 9999 by 360 gives a quotient of 27 and a remainder of 279. Subtracting 279 from 9999 yields 9720, and adding the required remainder of 11 gives the final result of 9731.

Keep practicing — related questions