Unit 1 number systems gcf and lcm
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Unit 1 – Number Systems GCF and LCM. Common multiples. Multiples of 6. Multiples of 8. 12. 60. 6. 18. 54. 66. 102…. 24. 24. 48. 48. 96. 96. 72. 8. 16. 32. 40. 56. 64. 72. 80. 88. 104 …. 30. 42. 78. 90. 84. 36. Multiples on a hundred square.

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Common multiples
Common multiples

Multiples of 6

Multiples of 8

12

60

6

18

54

66

102…

24

24

48

48

96

96

72

8

16

32

40

56

64

72

80

88

104 …

30

42

78

90

84

36



The least common multiple
The least common multiple

The least common multiple (or LCM) of two numbers is the smallest number that is a multiple of both the numbers.

We can find this by writing down the first few multiples for both numbers until we find a number that is in both lists.

For example:

100,

Multiples of 20 are :

20,

40,

60,

80,

120, . . .

25,

50,

75,

100,

125, . . .

Multiples of 25 are :

The LCM of 20 and 25 is

100.


The least common multiple1
The least common multiple

What is the least common multiple (LCM) of 8 and 10?

The first ten multiples of 8 are:

8,

16,

24,

32,

40,

48,

56,

64,

72,

80.

The first ten multiples of 10 are:

10,

20,

30,

40,

50,

60,

70,

80,

90,

100.

The least common multiple (LCM) of 8 and 10 is

40.


The least common multiple2
The least common multiple

5

5

and .

Add together

4

4

12

12

9

9

× 4

× 3

31

+

=

+

36

36

36

× 4

× 3

We use the least common multiplewhen adding and subtracting fractions.

The LCM of 9 and 12 is 36.

16

15

=



The greatest common factor
The greatest common factor

The greatest common factor (or GCF) of two numbers is the largest number that is a factor of both numbers.

We can find the greatest common factor of two numbers by writing down all their factors and finding the largest factor in both lists.

For example:

Factors of 36 are :

1,

2,

3,

4,

6,

9,

12,

18,

36.

Factors of 45 are :

1,

3,

5,

9,

15,

45.

The GCF of 36 and 45 is

9.


The greatest common factor1
The greatest common factor

What is the greatest common factor (GCF) of 24 and 30?

The factors of 24 are:

1,

2,

3,

4,

6,

8,

12,

24.

The factors of 30 are:

1,

2,

3,

5,

6,

10,

15,

30.

The greatest common factor (GCF) of 24 and 30 is

6.


The greatest common factor2
The greatest common factor

36

36

48

48

÷12

÷12

We use the greatest common factor when simplifying fractions.

Simplify the fraction .

The GCF of 36 and 48 is 12, so we need to divide the numerator and the denominator by 12.

3

=

4


Using prime factors to find the gcf and lcm
Using prime factors to find the GCF and LCM

2

60

2

294

1

1

We can use the prime factorization to find the GCF and LCM of larger numbers.

Find the GCF and the LCM of 60 and 294.

2

30

3

147

3

15

7

49

5

5

7

7

60 = 2 × 2 × 3 × 5

294 = 2 × 3 × 7 × 7


Using prime factors to find the gcf and lcm1
Using prime factors to find the GCF and LCM

60 = 2 × 2 × 3 × 5

294 = 2 × 3 × 7 × 7

60

294

2

7

2

3

5

7

GCF of 60 and 294 =

2 × 3

= 6

LCM of 60 and 294 =

2 × 5 × 2 × 3 × 7 × 7 =

2940



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