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March 28, 2017

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The gcf(a,b) = 495 and lcm( a,b) =31,185 Find possible values of a and b if a is divisible by 35 and b is divisible by 81.

  • factors math - ,

    This is a problem that requires the understanding of the relationship between LCM and GCF.
    Take the example of 45 and 63:
    45=9*5
    63=9*7
    GCF=9
    LCM=9*5*7
    So you see that GCF*LCM equals the products of the two numbers.

    Conversely, LCM/GCF is the product of factors NOT common to both (shown in bold in the above example).

    To find numbers a,b which have given LCM and GCF, divide M=LCM/GCF and distribute factors of M to the GCF, for example,
    LCM/GCF=9*7*5/9=7*5
    Multiplying the GCF by each of the factors gives the original numbers:
    9*7=63
    9*5=45.

    For the given case,
    LCM=31185
    GCF=495
    LCM/GCF=63=7*9
    So multiplying the GCF each by 7 and 9 will give the numbers a and b.

    GCF=9*

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  • factors math - ,

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