How many numbers in the range from 300 to 900 are divisible by 7, 14, and 28?

Solution

ATQ;

If a number is a multiple of 7, 14, and 28, then the number is a multiple of the L.C.M of 7, 14, and 28.

L.C.M of 7, 14, and 28 = 28

Smallest multiple of 28 between 300 and 900 = 308

Largest multiple of 28 between 300 and 900 = 896

Common difference = 28

Let the required number of terms be 'n'.

So, 308 + (n - 1) × 28 = 896

Or, n - 1 = (896 - 308) ÷ 28 = 21

So, n = 21 + 1 = 22

So, there are 22 numbers between 300 and 900 which are multiples of 7, 14, and 28.