Find the largest number of four digits such that on dividing by 12, 15, 18 & 21 the remainders are 9, 12, 15 & 18 respectively.

8817

LCM of 12, 15, 18, 21 = 1260

Greatest 4 digit divisible by 12, 15, 18, 21 = 1260 × 7 = 8820

Check Difference b/w (12 & 9), (15 & 12), (18 & 15), (21 & 18) = 3

*Req. no. will be 3 less than the greatest four digit number.*

Therefore,

Req. no. = 8820 - 3 = 8817

⇒ 8817 is the largest number of four digits such that on dividing by 12, 15, 18 & 21 the remainders will be 9, 12, 15 & 18 respectively.