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Use of Venn Diagrams to find the GCF and LCM. Least Common Multiple. The smallest number that is a common multiple of two or more numbers. 2 x 8 = 16 (16 is a multiple of 2 and of 8) Ex. 12 : 12, 24 , 36, 48 , 60, 72, 84 8 : 8, 16, 24 , 32, 48 , 56

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least common multiple
Least Common Multiple
  • The smallest number that is a common multiple of two or more numbers.

2 x 8 = 16 (16 is a multiple of 2 and of 8)

    • Ex.
      • 12: 12, 24, 36, 48, 60, 72, 84
      • 8: 8, 16, 24, 32, 48, 56

24 is the smallest common multiple so LCM= 24

      • 4: 4, 8, 12, 16, 20, 24, 28, 32, 36
      • 3: 3, 6, 9, 12, 15, 18, 21, 24, 27

12 is the smallest common multiple so LCM= 12

greatest common factor
Greatest Common Factor
  • The greatest factor that two or more numbers have in common.

3 x 15 = 45 (3 is a factor)

    • Ex)
      • 45: 1, 3, 5, 9, 15, 45
      • 27: 1, 3, 9, 27

9 is the greatest factor 45 and 27 have in common so GCF= 9

slide4

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?
slide5

FACTOR TREES

24

60

4

15

6

4

2

2

2

3

2

2

3

5

Prime Factors have now been found.

prime factors
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

slide7

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

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

slide8

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 of24 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

slide10

Find the GCF and LCM of the following:

  • 6 and 15
  • 20 and 30
  • 14 and 42
  • 24, 30 and 54
  • Answers:
  • GCF = 3, LCM = 30
  • GCF = 10, LCM = 60
  • GCF = 14, LCM = 42
  • GCF = 6, LCM = 1080