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Hương Yêu Dấu

20/08/2017 at 20:25
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How many of the first 500 positive integers are multiples of all three integers 3, 4 and 5?




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  • ...
    Help you solve math 20/08/2017 at 20:28

    Multiplies of 3,4,5 => Multiplies of 60 (3.4.5)

    So the numbers satisfy is: 60,120,180,240,300,360,420,480.60,120,180,240,300,360,420,480.So there are 8 positive integers satisfy the questionhaha

    Hương Yêu Dấu selected this answer.
  • ...
    Luffy xyz 123 20/08/2017 at 20:51

    I don't know this question

    Because i don't very good at English

    Sorry so much.

  • ...
    Help you solve math 20/08/2017 at 20:40

     Dao Trong Luan was wrong

  • ...
    Dao Trong Luan 20/08/2017 at 20:35

    Tell the numbers of this answer is a

    => a\(⋮3,4,5\) and \(0\le a\le499\)

    We have:

    3 = 3

    4 = 22

    5 = 5

    => \(LCM\left(3,4,5\right)=2^2.3.5=60\)

    => The multiples of all numbers 3, 4 and 5 is multiples of 60

    => a \(\in\left\{0,60,120,180,240,300,360,420,480,...\right\}\)

    But \(0\le a\le499\)

    => a \(\in\left\{0,60,120,180,240,300,360,420,480\right\}\)

    So there are 9 numbers


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