This document discusses determining common multiples and common factors of numbers. It explains that the common multiples of two numbers are the multiples that are shared between the two lists of all their individual multiples. The least common multiple is the smallest number that is a multiple of both numbers. It also explains that common factors are factors that two numbers have in common, and these can be determined by making lists of all the factors of each number and looking for the ones they share. A Venn diagram can also be used to visualize common factors between two numbers.

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

6. LEAST COMMON MULTIPLE

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?