Find the least number of five digits which when divided by 40, 60, and 75, leave remainders 31, 51 and 66 respectively.

Answer: Option C

Difference, 40 - 31 = 9
60 - 51 = 9
75 - 66 = 9
Difference between numbers and remainder is same in each case.
Then,
The answer = {(LCM of 40, 60, 75) - 9}

40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
LCM = 2 × 2 × 2 × 5 × 5 × 3 = 600
But, the least number of 5 digits = 10000
$$\frac{10000}{600},$$   we get remainder as 400
Then, the answer = 1000 - (600 - 400) - 9 = 10191