# factors math

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.

1. 👍
2. 👎
3. 👁
1. 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*

1. 👍
2. 👎
2. find a pair of numbers for each set of conditions.the LCM is 35.the GCF is 7.

1. 👍
2. 👎
3. What is the greatest common factor of 23, 40, and 43?

1. 👍
2. 👎
4. find a pair of numbers that matches the descripion . the LCM of two numbers is 42 and their sum is 20

1. 👍
2. 👎

## Similar Questions

1. ### Math

GCF of 2 natural numbers is 3 and their LCM is 180 if one of the numbers is 45 then find second number

2. ### maths

the gcf of two numbers is 3 and lcm is 180.if one of the numbers is 45,what is the other number?

3. ### math

The product of two numbers is 180. The LCM of the two numbers is 60. What is the GCF of the two numbers? How do you know?

4. ### Math

If p and q are relatively prime, then GCF(p,q) = ______, and LCM(p,q) = _______.

1. ### Math

Find the LCM and GCF of the following numbers: 1) 2016 and 756 2) 10140 and 705551 3) 17 664 and 288 4) 3960, 150 and 495 I believe the answers are: 1) LCM = 6048 GCF = 252 2) LCM = 7 154 287 140 GCF = 1 3) LCM = 52 992 GCF = 2208

2. ### Maths

Two number LCM is 495 & Two number HCF is 5. When we do Plus those number we find 100 number what diffrance bitween those number.

3. ### math6

the lcm is 30 the gcf is 2 whats the pair of numbers for each set of conditions

4. ### Algebra

Factor the GCF out of 5x2 - 10x? I know I need to find the GCF of the coefficients but I need to write it using the distributive property. Help please?

1. ### Algebra 1B

1.) Find the GCF of -25a3b4, 45a6b5. I got 25a3b4 2.)Find the GCF of a5b, a3b4, a2b3. I got a2b 3.) Find the GCF of 10ab5, 12a3b4, 16a2b3. I got 2ab3

2. ### Algebra

Find the GCF of each product. (6y^2-3y)(y+7) I think it is 3y. I'm not sure maybe there is no GCF in this problem. Any help would be appreciated.

3. ### MATH

Given the GCF or LCM, what else do you know about each pair of numbers? a) Two numbers have GCF of 2. b) Two numbers have an LCM of 2. Please and thankyou!

4. ### Math

Write a list of steps that are needed to find the measure of angle B. A measures 72 degrees and C measures 113. What does B measure? My Equation Answer: b=180-(a+c) 72+113=185 180-185= -5 My Word Answer: When you need to find the