Posted by **kendra** on Tuesday, November 29, 2011 at 6:33pm.

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**, Tuesday, November 29, 2011 at 8:41pm
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**, Thursday, February 2, 2012 at 5:39pm
find a pair of numbers for each set of conditions.the LCM is 35.the GCF is 7.

- factors math -
**baraa**, Wednesday, October 17, 2012 at 8:55pm
What is the greatest common factor of 23, 40, and 43?

- factors math -
**lulwa**, Saturday, December 8, 2012 at 6:53am
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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