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COMMON MULTIPLES
       &
 COMMON FACTORS


                   Created
                      by
                   tbonnar.
CH. 1.6
DETERMINING
    COMMON
  MULTIPLES
DETERMINING COMMON MULTIPLES

What are the common multiples of 3 and 4?
           Multiples of 3          Multiples of 4
    1x3=3                   1x4=4
    2x3=6                   2x4=8
    3x3=9                   3 x 4 = 12
    4 x 3 = 12              4 x 4 = 16
    5 x 3 = 15              5 x 4 = 20
    6 x 3 = 18              6 x 4 = 24
    7 x 3 = 21              7 x 4 = 28
    8 x 3 = 24              8 x 4 = 32

Are there any multiples in common?
DETERMINING COMMON MULTIPLES

 What are the common multiples of 5 and 6? We
  don’t need to make a chart every time. It is
  alright to just make a list.

 Multiples of 5
   5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

 Multiples of 6
   6, 12, 18, 24, 30, 36, 42, 48, 54, 60

 Any multiples in common?
LEAST COMMON MULTIPLE

The LCM (Least Common Multiple) is the
 smallest number that is a multiple of both
 numbers.
            Multiples of 3          Multiples of 4
     1x3=3                   1x4=4
     2x3=6                   2x4=8
     3x3=9                   3 x 4 = 12
     4 x 3 = 12              4 x 4 = 16
     5 x 3 = 15              5 x 4 = 20
     6 x 3 = 18              6 x 4 = 24
     7 x 3 = 21              7 x 4 = 28
     8 x 3 = 24              8 x 4 = 32
LEAST COMMON MULTIPLE
LEAST COMMON MULTIPLE

The LCM (Least Common Multiple) is the
 smallest number that is a multiple of both
 numbers.

Multiples of 5
  5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60


Multiples of 6
  6, 12, 18, 24, 30, 36, 42, 48, 54, 60
CH. 1.7
DETERMINING
    COMMON
    FACTORS
DETERMINING FACTORS

Recall: every number has factors (that means
 two numbers that multiply together to equal
 that number)
Example: Factors of 12
 1 x 12 = 12
 2 x 6 = 12
 3 x 4 = 12
So, 1, 2, 3, 4, 6, and 12 are all factors of 12
COMMON FACTORS – MAKING LISTS

If two numbers have the same factors, they
 are said to have common factors.
One way to determine common factors of
 numbers is to make lists of the factors.
COMMON FACTORS – MAKING LISTS

Another example:
COMMON FACTORS – MAKING LISTS
COMMON FACTORS –
USING VENN DIAGRAMS

             What does this
              Venn Diagram
              show us?
             What can we
              learn about
              common
              factors from it?

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Common Multiples and Common Factors

  • 1. COMMON MULTIPLES & COMMON FACTORS Created by tbonnar.
  • 2. CH. 1.6 DETERMINING COMMON MULTIPLES
  • 3. DETERMINING COMMON MULTIPLES What are the common multiples of 3 and 4? Multiples of 3 Multiples of 4 1x3=3 1x4=4 2x3=6 2x4=8 3x3=9 3 x 4 = 12 4 x 3 = 12 4 x 4 = 16 5 x 3 = 15 5 x 4 = 20 6 x 3 = 18 6 x 4 = 24 7 x 3 = 21 7 x 4 = 28 8 x 3 = 24 8 x 4 = 32 Are there any multiples in common?
  • 4. DETERMINING COMMON MULTIPLES  What are the common multiples of 5 and 6? We don’t need to make a chart every time. It is alright to just make a list.  Multiples of 5  5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60  Multiples of 6  6, 12, 18, 24, 30, 36, 42, 48, 54, 60  Any multiples in common?
  • 5. LEAST COMMON MULTIPLE The LCM (Least Common Multiple) is the smallest number that is a multiple of both numbers. Multiples of 3 Multiples of 4 1x3=3 1x4=4 2x3=6 2x4=8 3x3=9 3 x 4 = 12 4 x 3 = 12 4 x 4 = 16 5 x 3 = 15 5 x 4 = 20 6 x 3 = 18 6 x 4 = 24 7 x 3 = 21 7 x 4 = 28 8 x 3 = 24 8 x 4 = 32
  • 7. LEAST COMMON MULTIPLE The LCM (Least Common Multiple) is the smallest number that is a multiple of both numbers. Multiples of 5  5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 Multiples of 6  6, 12, 18, 24, 30, 36, 42, 48, 54, 60
  • 8. CH. 1.7 DETERMINING COMMON FACTORS
  • 9. DETERMINING FACTORS Recall: every number has factors (that means two numbers that multiply together to equal that number) Example: Factors of 12 1 x 12 = 12 2 x 6 = 12 3 x 4 = 12 So, 1, 2, 3, 4, 6, and 12 are all factors of 12
  • 10. COMMON FACTORS – MAKING LISTS If two numbers have the same factors, they are said to have common factors. One way to determine common factors of numbers is to make lists of the factors.
  • 11. COMMON FACTORS – MAKING LISTS Another example:
  • 12. COMMON FACTORS – MAKING LISTS
  • 13. COMMON FACTORS – USING VENN DIAGRAMS What does this Venn Diagram show us? What can we learn about common factors from it?