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    Two numbers have common factors of 216 and 540 and are multiples of 9 and 12. What are these two numbers? I can answer this question and figure out the answer as being 108 and 36, but my method is quite long, which is why I was wondering how other people would go out answering the question...
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    Moved to maths.
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    (Original post by neharajput)
    Two numbers have common factors of 216 and 540 and are multiples of 9 and 12. What are these two numbers? I can answer this question and figure out the answer as being 108 and 36, but my method is quite long, which is why I was wondering how other people would go out answering the question...
    How does 108 and 36 have a common factor of 216 and 540...?
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    (Original post by neharajput)
    Two numbers have common factors of 216 and 540 and are multiples of 9 and 12. What are these two numbers? I can answer this question and figure out the answer as being 108 and 36, but my method is quite long, which is why I was wondering how other people would go out answering the question...
    Should that word be 'are'?
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    (Original post by neharajput)
    Two numbers are common factors of 216 and 540 and are multiples of 9 and 12. What are these two numbers? I can answer this question and figure out the answer as being 108 and 36, but my method is quite long, which is why I was wondering how other people would go out answering the question...
    My method;

    Let A = numbers required

    first acknowledge that A is a multiple of 9 and 12

    L.C.M. of 9 & 12 = 36

    therefore A takes the form 36n (where n is > 0 and an integer)

    then think about the multiples of A, 540 and 216

    540 / 36 = 15
    216 / 36 = 6

    therefore n must be a factor of both 15 and 6

    n = 1 and 3 only

    therefore A = 36(1) and 36(3) = 36 and 108

    as required.
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    (Original post by neharajput)
    Two numbers have common factors of 216 and 540 and are multiples of 9 and 12. What are these two numbers? I can answer this question and figure out the answer as being 108 and 36, but my method is quite long, which is why I was wondering how other people would go out answering the question...
    Assuming a typo, this question becomes a lot simpler if you write each number as products of their prime factors.

    Have you tried this?
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    (Original post by Zacken)
    How does 108 and 36 have a common factor of 216 and 540...?
    I accidentally typed have, but I meant to say are
 
 
 
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