factors math

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.

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  1. 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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  2. find a pair of numbers for each set of conditions.the LCM is 35.the GCF is 7.

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  3. What is the greatest common factor of 23, 40, and 43?

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  4. find a pair of numbers that matches the descripion . the LCM of two numbers is 42 and their sum is 20

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