Finding the LCM and HCF Using the Product of Prime...
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  • Introduction
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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 x 32 x 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 smilar way, we find that 2100 = 22 x 3 x 52 x 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 x 2 x 5 x 5 x 3 = 300

 

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

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

 

  • Question 1
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Find the LCM of the following pair of numbers:

16 and 20

  • Question 2
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Find the HCF of the following pair of numbers:

16 and 20

  • Question 3
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Find the LCM of the following pair of numbers:

40 and 60

  • Question 4
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Find the HCF of the following pair of numbers:

40 and 60

  • Question 5
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Find the LCM of the following pair of numbers:

594 and 864

  • Question 6
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Find the HCF of the following pair of numbers:

594 and 864

  • Question 7
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Find the LCM of the following pair of numbers:

1071 and 1575

  • Question 8
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Find the HCF of the following pair of numbers:

1071 and 1575

  • Question 9
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Find the LCM of the following pair of numbers:

1500 and 390

  • Question 10
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Find the HCF of the following pair of numbers:

1500 and 390

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