posted by kendra on .
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.
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