Answer:
375
Explanation:
You want to know the number of integers from 1 to 1000 that are multiples of 4 or 6.
Multiples
Assuming the ends of the range are not multiples of interest, we can find the number of multiples of a given number by dividing the range by that number. Doing this for 4, 6, and (4×6), we find that in [1, 1000], there are ...
- 250 multiples of 4
- 166 multiples of 6
- 41 multiples of both 4 and 6
The number of multiples of 4 or 6 will be the total of multiples of 4 and multiples of 6, less the number of multiples of both 4 and 6. That is, the first sum counts those multiples of 24 twice.
250 +166 -41 = 375
There are 375 multiples of 4 or 6 in the range 1 to 1000.
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