mathschallenge.net

Problem

How many numbers below one hundred are divisible by both 2 and 3?

Solution

If the number is divisible by both 2 and 3 it will be divisible by 6.
16 6 = 96 (17 6 = 102)

So there are 16 numbers under 100 that are divisible by both 2 and 3.

How many numbers under 100 are divisible by 2, 3 and 4?

What about being divisible by 2, 3, 4 and 5?

How many numbers under n are divisible by the integers 1 to m?