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Math Help - counting numbers

  1. #1
    Newbie pinky&thebrain's Avatar
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    counting numbers

    How do i know if 360 is the smallest counting number divisible by all of 4,6,9,and 10
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Pinky&The Brain View Post
    How do i know if 360 is the smallest counting number divisible by all of 4,6,9,and 10
    It isn't 180 is.

    Look at the prime factorisations of 4, 6, 9, and 10, we have:

    4=2^2,
    6=2*3,
    9=3*3,
    10=2*5.

    So anything divisible by all these numbers must be divisible by:

    2^2*3^2*5=180

    so 180 is the least of these.

    RonL
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  3. #3
    Newbie pinky&thebrain's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    So anything divisible by all these numbers must be divisible by:

    2^2*3^2*5=180

    so 180 is the least of these.

    RonL

    I do not understand what you did here.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Pinky&The Brain View Post
    I do not understand what you did here.
    I took all the prime factors of the numbers in the list with the maximum
    multiplicity that they appear with in any one number, and then multiplied
    them together to find the required number.

    It is clear that as 4=2*2, then 2 must appear at least twice in the
    factorisation of the desired number, and as it appears no more times
    in any one of the factorisations of the numbers in the list it must appear
    exactly twice in the prime decomposition of the desired number.

    Same for 9=3*3.

    The only prime factor of a number in the list now unaccounted for is 5,
    so we must have one of those as well.

    RonL
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  5. #5
    Newbie pinky&thebrain's Avatar
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    Thanks... I got it now!
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