GCF with 3 numbers

1
GCF with 3 numbers LCM

• Lesson 4-4 4-5

2
Todays Math Standard

• Number Sense 2.4
• Determine the least common multiple and the
  greatest common divisor of whole numbers use
  them to solve problems with fractions (e.g., to
  find a common denominator to add two fractions or
  to find the reduced form for a fraction).

3
Steps to finding the GCF

• Make a factor tree for each of the numbers
• Write out the prime factorization of each number
• Write the factors from least to greatest
• Make a Venn diagram with 3 circles
• Place the exponents in the correct part of the
  Venn
• Look at the overlap area of the Venn diagram
• If there are no factors, then the GCF is 1
• If there is one factor, then that is the GCF
• If there is more than one factor, then multiply
  all the factors together

4
What is the GCF of 45, 60 and 96?
5
Make factor trees for each of the three numbers,
and write down their prime factors (without
exponents)
45 3 x 3 x 5
60 2 x 2 x 3 x 5
96 2 x 2 x 2 x 2 x 2 x 3
6
Lets explore the Venn diagram before we get
started
7
45 3 x 3 x 5
60 2 x 2 x 3 x 5
96 2 x 2 x 2 x 2 x 2 x 3
The GCF (or GCD) will ALWAYS be here. If you
dont see any numbers here, the GCF is 1!
45 60
60only
45only
All 3
45 96
60 96
96only
8
45 3 x 3 x 5
60 2 x 2 x 3 x 5
96 2 x 2 x 2 x 2 x 2 x 3
60
45
3
5
3
2
2
2
2
2
96
GCF 3
9
45 3 x 3 x 5
60 2 x 2 x 3 x 5
96 2 x 2 x 2 x 2 x 2 x 3
60
45
3
5
3
2
2
2
2
2
96
GCF 3
10
And while we have our Venn diagrams set up, lets
find the LCM
11
60
45
3
5
3
2
2
2
2
2
96
12
60
45
3
5
3
3
2
2
2
2
2
96
To Find the LCM Multiply all of the factors in
the Venn diagram together.
1440

?
?
?
?
?
?
?
The LCM of 45, 60, and 96 is 1440
13
What is the GCF of 7, 14 and 49?
14
Make factor trees for each of the three numbers,
and write down their prime factors (without
exponents)
7 7
14 2 x 7
49 7 x 7
15
Lets explore the Venn diagram before we get
started
16
7 7
The GCF (or GCD) will ALWAYS be here. If you
dont see any numbers here, the GCF is 1!
14 2 x 7
49 7 x 7
7 14
14only
7only
All 3
7 49
14 49
49only
17
7 7
14 2 x 7
49 7 x 7
14
7
2
7
7
49
GCF 7
18
And while we have our Venn diagrams set up, lets
find the LCM
19
14
7
2
7
7
49
20
14
7
2
7
7
49
To Find the LCM Multiply all of the factors in
the Venn diagram together.
98

?
?
The LCM of 7, 14, and 49 is 98
21
Note You can find the LCM for 2 numbers, too!

• Find the prime factorizations of both numbers
• Make a 2 circle Venn Diagram
• Place all numbers correctly
• Multiply ALL numbers

22
Find the GCF and LCM for 24 and 30
24 2 x 2 x 2 x 3
30 2 x 3 x 5
30
24
2
2
5
2
3
23
Find the GCF and LCM for 24 and 30
24 2 x 2 x 2 x 3
30 2 x 3 x 5
30
24
2
2
5
2
3
GCF 2 x 3
6
LCM 2 x 2 x 2 x 3 x 5
120
24
Lets Practice
25
Find the LCM and GCF for 21, 63, and 84
21 3 x 7
63 3 x 3 x 7
84 2 x 2 x 3 x 7

• GCF 21

LCM 252
26
Find the LCM and GCF for 42, 70, and 84
42 2 x 3 x 7
70 2 x 5 x 7
84 2 x 2 x 3 x 7

• GCF 14

LCM 420
27
An Alternative Method
28
This method is a variation of The Slide

• Click here to see it on YouTube.