Question

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.

Answer 1

This is a problem that requires the understanding of the relationship between LCM and GCF.
Take the example of 45 and 63:
45=<i>9</i>*<b>5</b>
63=<i>9</i>*<b>7</b>
GCF=<i>9</i>
LCM=<i>9</i>*<b>5*7</b>
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*

Answer 2

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

Answer 3

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

Answer 4

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