SOLUTION: How many positive integers less than or equal to 100 are multiples of 3 or multiples of 5 or multiples of both 3 and 5?

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Question 1009572: How many positive integers less than or equal to 100 are multiples of 3 or multiples of 5 or multiples of both 3 and 5?
Answer by KMST(5328) About Me  (Show Source):
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100%2F3=33%261%2F3 , so there are 33 integers less than or equal to 100 that are multiples of 3.
They are
1%2A3=3 , 2%2A3=6 ,3%2A3=9 , ... , 32%2A3=96 , and 33%2A3=99 .

100%2F5=20 , so there are 20 integers less than or equal to 100 that are multiples of 5.
They are
1%2A5=5 , 2%2A5=10 ,3%2A5=15 , ... , 19%2A5=95 , and 20%2A5=100 .
Of those 20 , there are some that are multiples of both 3 and 5,
and they are counted twice in the 33%2B20 multiples of 3 or multiples of 5 listed above.

Positive integers that are multiples of both 3 and 5, are multiples of 3%2A5=15 .
100%2F15=6 , so there are 6 integers less than or equal to 100 that are multiples of 15 (multiples of both 3 and 5).
They are
1%2A15=15 , 2%2A15=30 ,3%2A15=45 , 4%2A15=60 , 5%2A15=75 , and 6%2A15=90 .

The number of positive integers less than or equal to 100 that are
multiples of 3 or multiples of 5 or multiples of both 3 and 5 is
33%2B20-6=highlight%2847%29 .