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Unit 1 – Number SystemsGCF and LCM

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Multiples of 6

Multiples of 8

24 48 72 968 16 32 40 56 64 80 88 104 …

612

18

24

3036

42

48

5460

66

72

7884

90

96

102…

Common multiples

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Multiples on a hundred square

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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:

Multiples of 20 are : 20, 40, 60, 80, 100, 120, . . .

Multiples of 25 are : 25, 50, 75, 100, 125, . . .

The LCM of 20 and 25 is 100.

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.

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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.

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

The least common multiple

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We use the least common multiple when adding and subtracting fractions.

Add together 4

9

5

12and .

The LCM of 9 and 12 is 36.

+4

9

5

12=

36

× 4

× 4

16+

36

× 3

× 3

15=

31

36

The least common multiple

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Common factor diagram

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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 factor

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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 factor

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We use the greatest common factor when simplifying fractions.

Simplify the fraction .36

48

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

36

48=

÷12

3

÷12

4

The greatest common factor

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1

2942

1

602

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.

30215355

60 = 2 × 2 × 3 × 5

147349777

294 = 2 × 3 × 7 × 7

Using prime factors to find the GCF and LCM

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60 = 2 × 2 × 3 × 5

294 = 2 × 3 × 7 × 7

22

35

7

7

GCF of 60 and 294 = 2 × 3 = 6

LCM of 60 and 294 = 2 × 5 × 2 × 3 × 7 × 7 = 2940

Using prime factors to find the GCF and LCM

60 294

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Using prime factors to find the GCF and LCM