Transcript Use of Venn Diagrams to find the HCF and LCM

Chapter 5.1-5.3
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.
Let’s see if you were correct.
 Match the terms to the definitions shown below.
Prime Number
A whole number
greater than 1
whose only factors
are 1 and itself
Common Factor
Factor
A number that is a
A number that is
factor of two or more
multiplied by
numbers
another number to
LCM
find a product
The smallest
Prime Factor
Multiple
number, other than
Prime numbers that
The product of a
zero, that is a
are factors of an
given whole number
common multiple of
integer
and another whole
two or more
GCF
number
numbers
The greatest factor
Common Multiple
that two or more
A number that is a
numbers have in
multiple of two or
common
more numbers
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?
FACTOR TREES
24
4
2
60
6
22
4
3
2
15
2 3
Prime Factors have now been found.

5
Prime Factors
 24 = 2 x 2 x 2 x 3
 60 = 2 x 2 x 3 x 5
We now need to find the - Greatest Common Factor
GCF
and the LCM
- Least Common Multiple
Venn Diagram
GCF is the
region of
intersection
2 x 2 x 3 = 12
24 = 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
60
24
2
2
2
3
GCF = 2 x 2 x 3 = 12
LCM = 2 x 2 x 2 x 3 x 5 = 120
5
LCM is all the
numbers in the circles
multiplied together
2 x 2 x 2 x 3 x 5=120
The LCM of two or more numbers is the
smallest number that is a multiple of each
of the numbers.
24 x 5 =120
60 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 = 2
60 ÷ 12 = 5
Can you do some questions
now on your own?
Find the GCF and LCM of the following:
1. 6 and 15
2. 20 and 30
3. 14 and 42
4. 24, 30 and 54
Answers:
1.GCF = 3, LCM = 30
2.GCF = 10, LCM = 60
3.GCF = 14, LCM = 42
4.GCF = 6, LCM = 1080