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How many integers from 1 through 1,000 are multiples of 4 or multiples of 6?

User SleepyMurph
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1 Answer

23 votes
23 votes

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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How many integers from 1 through 1,000 are multiples of 4 or multiples of 6?-example-1
User Bart Van Nierop
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