How many integers in the range 1 through 140 are integer multiples of 2, 5, or 7?

Solution:

If the numbers from 1-140 are considered

We will have 70 integers for 2

We will have 28 integers for 5, but integers which end with 0 are integers of 2 and reduces the number added to 14.

The numbers 7, 14, 21, 28, 35, 42, 49, 56, 63 and 70 are the multiples of 7 from 1-70.

The same pattern is repeated from 71-140.

So there are 20 integers in all.

Anyhow, 12 of the multiples are multiples of either 2 or 5 which reduces the number to 8 integers.

So from 1-140, the integers of 2, 5 or 7 = 70 + 14 + 8 = 92 integers

Therefore, the integers in the range 1 through 140 is 92.

How many integers in the range 1 through 140 are integer multiples of 2, 5, or 7?

Summary:

The integers in the range 1 through 140 which are integer multiples of 2, 5, or 7 is 92.