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.

factors math 
MathMate,
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* 
factors math 
maf,
find a pair of numbers for each set of conditions.the LCM is 35.the GCF is 7.

factors math 
baraa,
What is the greatest common factor of 23, 40, and 43?

factors math 
lulwa,
find a pair of numbers that matches the descripion . the LCM of two numbers is 42 and their sum is 20