It is possible to use a Venn diagram to help find the GCF and LCM of two numbers?

Question

For example, to find the GCF and LCM of the numbers 48 and 66, you would find the prime factorization of each and organize the factors in such a way that the common factors went into the overlap of the two circles representing 48 and 66. The GCF is 6.

 

a) How could you also find the LCM?

b) Use this technique to represent and find the GCF and LCM of 56 and 91.

 

Answer 1

Here's something else that might help in finding GCF and LCM of 2 numbers...

The product of the 2 numbers divided by the LCM gives you the GCF.

The product of the 2 numbers divided by the GCF gives you the LCM.

In your examples, 48 and 66, the GCF=6 and the LCM=528.

48*66=3168, 3168/6=528, and 3168/528=6

56*91=5096, 5096/7=728 which is the LCM

Another example: 24 and 36, LCM=72 and GCF=12

24*36=864, 864/12=72, and 864/72=12

If you can find one and not the other, multiply the numbers together and divide by the one you can find.

Don't forget, we are talking about the GCF and LCM of "2" numbers, not of 3 or 4, or more.

Hope this helps a little more.

Answer 2

Yes, you could. The LCM would then be the product of all of the numbers in the diagram, not counting the ones in the GCF more than once.

 

For your example:

48 = 2*2*2*2*3

66 = 2*3*11

 

"Venn diagram"

[ 48 = 2*2*2* ( 2*3 ] *11 = 66 )

the GCF is 6

the LCM is 8*6*11=528

 

For 56 and 91

56 = 2*2*2*7

91 = 7*13

 

"Venn diagram"

[ 56 = 2*2*2* ( 7 ] *13 = 91 )

GCF = 7

LCM = 8*7*13 = 728

Answer 3

Hi Taylor--see my answer to your other question.

 

GCF and LCM are actually used for very different purposes, so you wouldn't necessarily want them on the same diagram. And I don't think a Venn could help determine the factors or multiples--you could use one to SHOW them, but not really to help in actually figuring them out.

 

See my other answer for explanations of both and how to get them.

 

Cheers,

 

Matt in New York