Greatest Common Factors & Least Common Multiples

Methods for finding Greatest Common Factors

List the Factors:
Find GCF (16,56)

Factors of 16: 1,2,4,8,16
Factors of 56: 1,2,4,7,8,14,28,56

Now you look and find which number is a factor of both that is the highest or greatest number!

So in this case the highest number is 8... So the GCF (16,56) = 8

Linear (Cuisenaire rods)
Find GCF (6,12)
Find GCF (4,8)
Find GCF (4,9)


And for this all you do is put together the blocks that would make up the number your looking for. And then you will find the Great Common Factor for both.

Prime Factorization

Find GCF (30,42)

30= 2 x 3 x 5
Now how you find these prime factors

3 x 5 = 15
15 x 2 = 30

2,3,5 are all prime numbers

42= 2 x 3 x 7
SAME as the top

3 x 7 = 21
2 x 21 = 42

2,3,7 are all prime numbers they can't be divide down anymore.

Methods for finding Least Common Multiples

List the Multiples
Find LCM (3,5)

Multiples: 3,6,9,12,15,18,21
Multiples:5,10,15,20,25,30

And your least common multiple is 15 and for this one you can stop as soon as you find a common factor for both because your finding the lowest number.

Linear
Find LCM (4,5)

You can use the number line to help you with this type

And all you have to do is add the number to itself everytime.
 

Prime Factorization
Find LCM (8,20)

8: 2 x 2 x 2
20: 2 x 2 x 5

And this is how you get these numbers.
2 x 2 = 4
4 x 2 = 8

2 x 5 = 10
10 x 2 = 20

You always keep dividing until you can't divide anymore.