The ABC’s of GCF and LCM
GCF = Greatest Common Factor
• If the word factor is in the name, I know
this has to do with multiplication.
• Greatest obviously means the factor with
the largest value
• Common must mean more than one
number has this single factor
Greatest Common Factor
• The Greatest Common Factor is the largest
factor two or more numbers share
• How do you find the GCF of 12 and 18?
▫ Using the rules of divisibility, find all of the factors
of 12 and 18
 12= 1, 2, 3, 4, 6, 12
 18 = 1, 2, 3, 6, 9, 18
Greatest Common Factor
12= 1, 2, 3, 4, 6, 12
18 = 1, 2, 3, 6, 9, 18
• Find the numbers that occur in both lists
• Choose the number that is the largest
• The Greatest Common Factor of 12 and 18
is 6
Greatest Common Factor
• Find the GCF between 75 and 30
• Use the rules of divisibility to help you
75 –ends in 5
- digits add to 12 (which is divisible by 3)
- follows the identity property
The factors of 75 are 1, 3, 5, 15, 25, 75
5 * 15
3 * 25
1* 75
Greatest Common Factor
• Find the GCF between 75 and 30
• Use the rules of divisibility to help you
30 –ends in 5 and 0
- is an even number
- follows the identity property
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
5*6
3 * 10
2 * 15
1* 30
Greatest Common Factor
• Compare the two strings of factors and find the
largest common factor:
75 = 1, 3, 5, 15, 25, 75
30 = 1, 2, 3, 5, 6, 10, 15, 30
The Greatest Common Factor is 15
Greatest Common Factor and Factor Trees
• Create factor trees for 18 and 30remember to divide down to the
prime factorization of each number
18
30
3*6
5*6
3*2
3*3*2
3*2
5*3*2
Greatest Common Factor and Factor Trees
18
3*6
3*2
3*3*2
30
5*6
3*2
5*3*2
• 3 and 2 are common in both prime
factorization, therefore 3*2 or 6 is
the GCF
Practice Time
• Math Journal 2 page3 405-407
• Math Practice Book 13.2
Least Common Multiple
• If the word multiple is in the name, I know this
has to do with multiplication
• A multiple is the product of two numbers that
are multiplied together
▫ 7*3 = 21
21 is the multiple of 7 and 3
• Least means I am looking for the smallest
multiple
• Common means the multiple must be included
in both numbers multiple strings
Least Common Multiple
• Find the Least Common Multiple of 4 and 6
• List the multiples in order for each number:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48…
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72…
What is the smallest number that sits in both
strings?
Least Common Multiple
• Find the Least Common Multiple of 4 and 6
• List the multiples in order for each number:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48…
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72…
What is the smallest number that sits in both
strings?
Least Common Multiple
• Find the LCM of:
6 and 8
24
3 and 8
6 and 9
24
18
Practice LCM
• Math Practice Book 13.3
Using Factor Trees to find the LCM
• Use factor trees to find the prime factorization for
18 and 30
18
3*6
3*2
3*3*2
30
5*6
3*2
5*3*2
• 3*2 repeats in both factor strings
Using Factor Trees to find the LCM
3*3*2
3*2*5
• 3*2 repeats in both factor strings
• Eliminate one set of 3 * 2 and multiply
the rest of the prime factors together
3*3*2*5
90
The LCM of 18 and 30 is 90
Greatest Common Factor and Factor Trees
18
3*6
3*2
3*3*2
30
5*6
3*2
5*3*2
• 3 and 2 are common in both prime
factorization, therefore 3*2 or 6 is
the GCF
Factoring out the LCM
• Find the LCM using factor tree method for:
12 and 42
32 and 20
16 and 24
84
160
48
Factoring out the LCM
•Practice this method
•Math Journal 2 page 408