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Multiples of either number

CombinatoricsEasy

How many integers from $1$ to $100$ are divisible by $4$ or by $6$ (or by both)?

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Hint

Add both counts of multiples, then fix the overlap.

Solution

There are $25$ multiples of $4$ and $16$ multiples of $6$ in this range.
A number divisible by both is a multiple of $12$ , and there are $8$ of those, counted in both lists.
The answer is $25 + 16 - 8 = 33$ .

Answer: $33$