How many positive integers not exceeding 100 are divisible either by 4 or by 6?

Solution:

We have to find the total number of positive integers not exceeding 100 that are divisible either by 4 or by 6.

Integers divisible by 4 are 

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96.

Integers divisible by 6 are 

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96.

Common terms which are divisible by both 4 and 6 are 

12, 24, 36, 48, 60, 72, 84, 96.

Total number of integers excluding the common terms is 32.

Therefore, 32 positive integers not exceeding 100 are divisible either by 4 or by 6.

How many positive integers not exceeding 100 are divisible either by 4 or by 6?

Summary:

32 positive integers not exceeding 100 are divisible either by 4 or by 6.