This is a problem that requires the understanding of the relationship between LCM and GCF.
Take the example of 45 and 63:
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,
Multiplying the GCF by each of the factors gives the original numbers:
For the given case,
So multiplying the GCF each by 7 and 9 will give the numbers a and b.
find a pair of numbers for each set of conditions.the LCM is 35.the GCF is 7.
What is the greatest common factor of 23, 40, and 43?
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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