Explanation:

If a number is divided by 12 and 40 then it must be divided by their LCM which is 120.
Numbers between 900 and 3000 which are divisible by 120 are
960, 1080,..., 2880.
i.e., the first number which is divisible by 120 and greater than 900 is 960.
The number 3000 is also divisible by 120 but we have to find the numbers between 900 and 3000.
So the last number which is divisible by 120 and less than 3000 is 2880.
The numbers are 960, 1080,.., 2880.
This is an A.P where a = 960, d = 120 and t(n) = 2880
We know that the n-th term in A.P = a + (n - 1)d
2880 = 960 + (n - 1)120
2880 = (8 + (n - 1))120
24 = 8 + n - 1
n = 17.
Hence, there are 17 numbers between 900 and 3000 that are exactly divisible by both 12 and 40.