Explanation:

Sol. Ans.(b).

Desired number = (Least multiple of four digit of LCM of 3, 4 and 5) + 2

So the LCM of 3, 4, 5 and 6 is 60.

The least 4-digit number divisible by 60 is 1020.

So with remainder 2 it will be 1020 + 2 = 1022. Answer is (b).

Alternative method: Work backward from the options and check all the options.