How many positive integers between 100 and 999 inclusive are divisible by three or four?

999 - 100 + 1 = 900

There are 900 numbers between 100 and 999 (inclusive)

We group the numbers into groups of 3s. So we find one number divisible by 3 in every group.

Number of numbers that can be divided by 3 = 900 : 3 = 300

Number of numbers that can be divided by 3 = 300

We group the numbers into groups of 4s. So we find one number divisible by 4 in every group.

Number of numbers that can divided by 4 = 900 : 4 = 225

Number of numbers that can divided by 4 = 225

Among the group of 4s, there is 1/3 that are already inclusive in divisible by 3.

225 : 3 = 75

Number of numbers that can divided by 4 = 225 - 75 = 150

Total numbers of positive integers divisible by three and fours = 300 + 150 = 450