Download HCF, LCM, prime factor tree

Highest Common Factor
Lowest Common Multiple
using prime factor trees
David Weeks
© www.Mathsmadeeasy.co.uk
Permission given to use for non-commercial use
Find the HCF of 60 and 72
Find the LCM of 60 and 72
Find the HCF of 48 and 56
Find the LCM of 48 and 56
Alter animation effects as appropriate – play as slide show
You will learn… how to
Make a Prime Factor Tree
Find the HCF of two numbers
Find the LCM of two numbers
Highest Common Factor HCF
Take two numbers
8
10
2
What’s the biggest number that will go into both?
2 goes into 8 four times 8 ÷ 2 = 4
2 goes into 10 five times 10 ÷ 2 = 5
There’s no bigger number than 2 that goes into both
So it’s the biggest FACTOR
or the Highest Common Factor
Lowest Common Multiple LCM
8
Take two numbers
40
10
If you do the times table for each at what number do they cross
1
2
3
4
5
6
7
8
8
16
24
32
40
48
56
64
10
20
30
40
50
60
70
80
The first time they cross is at 40
So it’s the Lowest Common Multiple
of these two numbers
Finding HCF and LCM
using the prime factor tree
Did you know?
EVERY number
is made from
Prime numbers
Multiplied together!
The first prime number is 2, then 3, then 5, then 7.
It’s a number that no other number goes into
except itself and one
Exercise
Find the HCF of 60 and 72
Find the LCM of 60 and 72
Prime Factor Tree for 60
60
Write 60 at the top of the page
60 = prime number 2 x 30
30 = prime number 2 x 15
15 = prime number 3 x prime number 5
30
2
15
2
3
5
60 is all the prime numbers 2 x 2 x 3 x 5 multiplied together
Prime Factor Tree for 72
72
Write 72 at the top of the page
72 = prime number 2 x 36
36 = prime number 2 x 18
18 = prime number 2 x 9
9 = prime number 3 x prime number 3
36
2
18
2
2
9
3
3
72 is the prime numbers 2 x 2 x 2 x 3 x 3 multiplied together
Finding the Highest Common Factor
72
60
2
30
2
x
15
2
3
18
2
2
5
36
2
x
2
3
Look for common factors in both trees
Multiply them together =
12
9
3
12 is the biggest number that goes into both 60 and 72
So it is the Highest Common Factor
3
Finding the Lowest Common Multiple
60
2
18
2
15
3
36
2
30
2
72
5 x 72 =360
5
2 x 3 x 60
=360
Look for the factors remaining in either tree
2
9
3
Cross multiply with top number in opposite tree
360 is the Lowest Common Multiple of 60 and 72
3
Finding the LCM with a Venn Diagram
Write out the prime factors you found for each number
60 = 5 × 3 × 2 × 2
72 = 2 × 2 × 3 × 2 × 3
2
5×
×
2
×2×3
×
3
Put the common factors in the middle
Then multiply everything to get the LCM
5 × 2 × 2 × 3 × 2 × 3 = 10 × 6 × 6 = 360
Exercise
Find the HCF of 56 and 48
Find the LCM of 56 and 48
Prime Factor Tree for 56
56
Write 56 at the top of the page
56 = prime number 2 x 28
28 = prime number 2 x 14
14 = prime number 2 x prime number 7
28
2
14
2
2
7
56 is all the prime numbers 2 x 2 x 2 x 7 multiplied together
Prime Factor Tree for 48
48
Write 48 at the top of the page
48 = prime number 2 x 24
24 = prime number 2 x 12
12 = prime number 2 x 6
6 = prime number 2 x prime number 3
24
2
12
2
2
6
2
3
48 is the prime numbers 2 x 2 x 2 x 2 x 3 multiplied together
Finding the Highest Common Factor
48
56
2
28
2
x
14
2
2
12
2
2
7
24
2
x
2
2
Look for common factors in both trees
Multiply them together =
8
6
2
8 is the biggest number that goes into both 56 and 48
So it is the Highest Common Factor
3
Finding the Lowest Common Multiple
56
2
12
2
14
2
24
2
28
2
48
7 x 48 =336
7
2 x 3 x56
=336
Look for the factors remaining in either tree
2
6
2
Cross multiply with top number in opposite tree
336 is the Lowest Common Multiple of 56 and 48
3
Finding the LCM with a Venn Diagram
Write out the prime factors you found for each number
56 = 7 × 2 × 2 × 2
48 = 2 × 2 × 2 × 2 × 3
2
7×
×
2
×2×3
×
2
Put the common factors in the middle
Then multiply everything to get the LCM
7 × 2 × 2 × 2 × 2 × 3 = 7 × 8 × 6 = 336
You now know… how to
Make a Prime Factor Tree
Find the HCF of two numbers
Find the LCM of two numbers