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How many multiple of 2, 3 and 5 are there between 1 and 6000?
One of the question of our (Italian) final math test that in these hours (from 9am to 3pm, Italian hour) thousands of students are doing
Yesterday they had (written) Italian... a kind of essay or something like that
2 Answers
- 7 years agoFavorite Answer
Actually this question isn't very simple.
Firstly you know they are 3000 multiples of 2, they are 2000 multiples of 3, 1200 multiples of 5.
Now we check for repeats. They are 1000 multiples of 2 and 3 (6), 400 multiples of 3 and 5 (15) and 600 multiples of 2 and 5 (10).
So 3000 + 2000 + 1200 - 1000 - 400 - 600
However some numbers are multiples of 2 and 3 and multiples of 3 and 5, they are hence multiples of 2 and 3 and 5. So you need to subtract these from the repeats. They are 200 of them.
Hence 3000 + 2000 + 1200 - (1000 + 400 + 600 - 200) = 4400
- 7 years ago
3000 multiples of 2 + 1000 unique multiples of 3 (because every other is even) + 40 unique multiples of 5 (because every other is a multiple of 2 and every third is a multiple of 3)
So, 4040, I think.
