 # Finding the LCM and HCF Using the Product of Prime Factors

In this worksheet, students find the lowest common multiple and highest common factor using the product of prime factors. Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Use Concepts and Vocabulary for All Numbers

Difficulty level:   ### QUESTION 1 of 10

In this worksheet, we will be finding the lowest common multiple (LCM) and the highest common factor (HCF) of two numbers using their products of prime factors.

Reminder

 This is how we write 1800 as the product of prime factors: 1800 = 23 × 32 × 52 2 1 8 0 0 2 9 0 0 2 4 5 0 3 2 2 5 3 7 5 5 2 5 5

In a similar way, we find that 2100 = 22 × 3 × 52 × 7

Example

Find the LCM and HCF of 1800 and 2100.

We can put all the prime factors in a Venn Diagram such as this: To find the HCF, we multiply together the numbers in the intersection.

HCF = 2 × 2 × 5 × 5 × 3 = 300

To find the LCM, we multiply all the numbers in the Venn Diagram

LCM = 2 × 2 × 2 × 3 × 3 × 5 × 5 × 7 = 1800 × 7 = 12600

Find the LCM of the following pair of numbers:

16 and 20

Find the HCF of the following pair of numbers:

16 and 20

Find the LCM of the following pair of numbers:

40 and 60

Find the HCF of the following pair of numbers:

40 and 60

Find the LCM of the following pair of numbers:

594 and 864

Find the HCF of the following pair of numbers:

594 and 864

Find the LCM of the following pair of numbers:

1071 and 1575

Find the HCF of the following pair of numbers:

1071 and 1575

Find the LCM of the following pair of numbers:

1500 and 390

Find the HCF of the following pair of numbers:

1500 and 390

• Question 1

Find the LCM of the following pair of numbers:

16 and 20

80
EDDIE SAYS

First we need to find the prime factors of each number
16 = 2 x 2 x 2 x 2
20 = 2 x 2 x 5

The HCF is given by the numbers that appear in both lists
HCF = 2 x 2 = 4

The LCM is given by the HCF multiplied by all the rest of the numbers

LCM = 2 x 2 x 2 x 2 x 5 = 80

• Question 2

Find the HCF of the following pair of numbers:

16 and 20

4
EDDIE SAYS

First we need to find the prime factors of each number
16 = 2 x 2 x 2 x 2
20 = 2 x 2 x 5

The HCF is given by the numbers that appear in both lists
HCF = 2 x 2 = 4

The LCM is given by the HCF multiplied by all the rest of the numbers

LCM = 2 x 2 x 2 x 2 x 5 = 80

• Question 3

Find the LCM of the following pair of numbers:

40 and 60

120
EDDIE SAYS

First we need to find the prime factors of each number
40 = 2 x 2 x 2 x 5
60 = 2 x 2 x 3 x 5

The HCF is given by the numbers that appear in both lists
HCF = 2 x 2 x 5 = 20

The LCM is given by the HCF multiplied by all the rest of the numbers

LCM = 2 x 2 x 5 x 2 x 3 = 120

• Question 4

Find the HCF of the following pair of numbers:

40 and 60

20
EDDIE SAYS

First we need to find the prime factors of each number
40 = 2 x 2 x 2 x 5
60 = 2 x 2 x 3 x 5

The HCF is given by the numbers that appear in both lists
HCF = 2 x 2 x 5 = 20

The LCM is given by the HCF multiplied by all the rest of the numbers

LCM = 2 x 2 x 5 x 2 x 3 = 120

• Question 5

Find the LCM of the following pair of numbers:

594 and 864

9504
EDDIE SAYS

First we need to find the prime factors of each number
594 = 2 x 3 x 3 x 3 x 11
864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

The HCF is given by the numbers that appear in both lists
HCF = 2 x 3 x 3 x 3  = 54

The LCM is given by the HCF multiplied by all the rest of the numbers

LCM = 2 x 3 x 3 x 3  x 11 x 2 x 2 x 2 x 2 = 9504

• Question 6

Find the HCF of the following pair of numbers:

594 and 864

54
EDDIE SAYS

First we need to find the prime factors of each number
594 = 2 x 3 x 3 x 3 x 11
864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

The HCF is given by the numbers that appear in both lists
HCF = 2 x 3 x 3 x 3  = 54

The LCM is given by the HCF multiplied by all the rest of the numbers

LCM = 2 x 3 x 3 x 3  x 11 x 2 x 2 x 2 x 2 = 9504

• Question 7

Find the LCM of the following pair of numbers:

1071 and 1575

26775
EDDIE SAYS

First we need to find the prime factors of each number
1071 = 3 x 3 x 7 x 17
1575 = 3 x 3 x 5 x 5 x 7

The HCF is given by the numbers that appear in both lists
HCF = 3 x 3 x 7  = 63

The LCM is given by the HCF multiplied by all the rest of the numbers

LCM = 3 x 3 x7  x 17 x 5 x 5 = 26775

• Question 8

Find the HCF of the following pair of numbers:

1071 and 1575

63
EDDIE SAYS

First we need to find the prime factors of each number
1071 = 3 x 3 x 7 x 17
1575 = 3 x 3 x 5 x 5 x 7

The HCF is given by the numbers that appear in both lists
HCF = 3 x 3 x 7  = 63

The LCM is given by the HCF multiplied by all the rest of the numbers

LCM = 3 x 3 x7  x 17 x 5 x 5 = 26775

• Question 9

Find the LCM of the following pair of numbers:

1500 and 390

19500
EDDIE SAYS

First we need to find the prime factors of each number
1500 = 2 x 2 x 3 x 5 x 5 x 5
390 = 2 x 3 x 5 x 13

The HCF is given by the numbers that appear in both lists
HCF = 2 x 3 x 5 = 30

The LCM is given by the HCF multiplied by all the rest of the numbers

LCM = 2 x 3 x 5 x 2 x 5 x 5 x 13 = 19500

• Question 10

Find the HCF of the following pair of numbers:

1500 and 390

30
EDDIE SAYS

First we need to find the prime factors of each number
1500 = 2 x 2 x 3 x 5 x 5 x 5
390 = 2 x 3 x 5 x 13

The HCF is given by the numbers that appear in both lists
HCF = 2 x 3 x 5 = 30

The LCM is given by the HCF multiplied by all the rest of the numbers

LCM = 2 x 3 x 5 x 2 x 5 x 5 x 13 = 19500

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