1. Use of Venn Diagrams to find the GCF and LCM
Chapter

2. Do you remember? The definition of: prime number? factor?
prime factor?
common factor?
greatest common factor?
multiple?
common multiple?
least common multiple?
Write these definitions in your own words on your MMC worksheet.

3. Let’s see if you were correct.
Match the terms to the definitions shown below.
Prime Number
Common Factor
A whole number greater than 1 whose only factors are 1 and itself
Factor
A number that is a factor of two or more numbers
A number that is multiplied by another number to find a product
LCM
The smallest number, other than zero, that is a common multiple of two or more numbers
Prime Factor
Multiple
Prime numbers that are factors of an integer
The product of a given whole number and another whole number
GCF
The greatest factor that two or more numbers have in common
Common Multiple
A number that is a multiple of two or more numbers

4. Find the GCF and LCM of 24 and 60
Use a factor tree to help you find the Prime Factors
Then a Venn Diagram to help you find the GCF and LCM
Can you remember how to draw a Factor Tree?

5. Prime Factors have now been found. 
FACTOR TREES 24 60 4 6 4 15 2 2 2 3 2 2 3 5
Prime Factors have now been found 

6. We now need to find the GCF
Prime Factors
24 = 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
We now need to find the GCF
- Greatest Common Factor
and the LCM
- Least Common Multiple

7. Venn Diagram GCF is the region of intersection 24 = 2 x 2 x 2 x 360 24 2 2 5 2
LCM is all the numbers in the circles multiplied together
2 x 2 x 2 x 3 x 5=120 3
GCF = 2 x 2 x 3 = 12
LCM = 2 x 2 x 2 x 3 x 5 = 120

8. or you could write out the multiples of 24 and 60
The LCM of two or more numbers is the smallest number that is a multiple of each of the numbers.
24 x 5 = x 2 =120
or you could write out the multiples of 24 and 60
24, 48, 72, 96, 120, 144,….
60, 120, 180, 240, 300,....
The GCF of two or more numbers is the largest number that divides exactly into each of them.
24 ÷ 12 = ÷ 12 = 5

9. Can you do some questions
now on your own?

10. Find the GCF and LCM of the following:
Answers:
GCF = 3, LCM = 30
GCF = 10, LCM = 60
GCF = 14, LCM = 42
GCF = 6, LCM = 1080