2023 · Q18
What is the largest 5-digit number, which leaves the remainder 7, when divided by 18 as well as by 11?
Elementary MathematicsNumber System
- A99981
- B99988
- C99997
- D99999
Explanation
The number is 7 modulo 18 and 7 modulo 11, hence 7 modulo lcm(18, 11) = 198. Numbers of the form 198k + 7 below 100000 go up to k = 505, giving 198 × 505 + 7 = 99997. This is the largest 5-digit number with the required property (C).