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**Use of Venn Diagrams to find the GCF and LCM**

Chapter

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**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.

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**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

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**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?

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**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

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**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

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**Venn Diagram GCF is the region of intersection 24 = 2 x 2 x 2 x 3**

60 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

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**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

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**Can you do some questions**

now on your own?

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**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

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