Find the least multiple of 23, which when divided by 18, 21 and 24 leaves the remainder 7, 10 and 13 respectively.

A. 3013

B. 3024

C. 3002

D. 3036

Answer: Option A

Solution(By Examveda Team)

18 - 7 = 11
21 - 10 = 11
24 - 13 = 11
Take LCM of (18, 21, 24)
⇒ 9 × 2 × 7 × 4 = 504
⇒ Required number = (504k - 11) which is divided by 23
∴ For $$\frac{{504k - 11}}{{23}},$$   remainder should be zero
Put minimum value of k so that it completely divides 23
⇒ at k = 6, 504k - 11 = 3013 completely divisible by 23
∴ Required number is = 3013