How many numbers in the range from 150 to 1000 are

Solution

ATQ;
If a number is a multiple of 5, 10, and 20, then the number is a multiple of the L.C.M of 5, 10, and 20.

L.C.M of 5, 10, and 20 = 20

Smallest multiple of 20 between 150 and 1000 = 160

Largest multiple of 20 between 150 and 1000 = 1000

Common difference = 20

Let the required number of terms be 'n'.

So, 160 + (n - 1) × 20 = 1000

Or, n - 1 = (1000 - 160) ÷ 20 = 42

So, n = 42 + 1 = 43

So, there are 43 numbers between 150 and 1000 which are multiples of 5, 10, and 20.