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

Answer: Option A

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