Explanation:

If a number is divided by 2,3 and 4 then it must be divided by their LCM 12 also.
Numbers between 100 and 1000 which are divisible by 12 are
108, 120,..., 996.
i.e., the first number which is divisible by 12 and greater than 100 is 108.
And the last number which is divisible by 12 and less than 1000 is 996.
Then the numbers are 108, 120,..., 996.
This is an A.P where a = 108, d = 12 and t(n) = 996
We know that the n-th term in A.P = a + (n-1)d
996 = 108 + (n-1)12
83 = 9 + n-1
n = 75.