Finding GCF’s and LCM’s

Grade 6

Do Now (Pre-Test)

Study Island Responders

5 minutes

Learning ObjectiveStudents will be able to identify factors and multiples of a positive integer, common factors, common multiples, the greatest common factor, and the least common multiple of a set of positive integers. 5N13 - Calculate multiples of a whole number and the least common multiple of two numbers 5N14 - Identify the factors of a given number 5N15 - Find the common factors and the greatest common factor of two numbers

Vocabulary

• GCF – the factor with the greatest value that is shared by all numbers.

• Multiples – the product of a number and a non zero number.

• LCM – the multiple with the least value that is shared by all numbers.

Finding the Greatest Common Factor

of Two Numbers

must be common to both numbers. WeWe are looking for a factor. The factor

need to pick the greatest of suchcommon factors.

Method 1

The GCF of 36 and 90

1) List the factors of each number.

36: 1 2 3 4 6

36 18 24 9

2) Circle the common factors.

90: 1 2 3 5 6 9

90 45 30 18 15 10

3) The greatest of these will be your Greatest Common Factor:

18

Method 2

The GCF of 36 and 90

1) Prime factor each number.

36 = 2 ● 2 ● 3 ● 3

2) Circle each pair of common prime factors.

90 = 2 ● 3 ● 3 ● 5

3) The product of these common prime factors will be

2 ● 3 ● 3 = 18the Greatest Common Factor:

Finding the Least Common Multiple

of Two Numbers

must be common to both numbers. WeWe are looking for a multiple. The multiple

need to pick the least of suchcommon multiples.

Method 1

The LCM of 12 and 15

1) List the first few multiples of each number.

12: 12 24 36 48 60 72 84 90 108 120

2) Circle the common multiples.

15: 15 30 45 60 75 90 105 120 135

3) The least of these will be your Least Common Multiple:

60

Method 2

The LCM of 12 and 15.

1) Prime factor each number.

12 = 2 ● 2 ● 3

2) Circle each pair of common prime factors.

15 = 5 ● 3

4) Multiply together one factor from each circle to get the

3 ● 2 ● 2 ● 5 = 60Least Common Multiple :

3) Circle each remaining prime factor.

Note that the common factor, 3, was only used once.

Method 3: Find both GCF and LCM at Once.

1) Make the following table.

72 90

The GCF and LCM of 72 and 90

2) Divide each number by a common factor.

3) Divide the new numbers by a common factor. Repeat this process until there is no longer a common factor.

9

8 1024 5

The product of the factors on the left is the GCF:

9 ● 2 = 18

The product of the factors on the left AND bottom is the LCM: 9 ● 2 ● 4 ● 5 = 360

Method 3: Find both GCF and LCM at Once.

1) Make the following table.

96 144

One more example: The GCF and LCM of 96 and 144

2) Divide each number by a common factor.3) Divide the new numbers by a common factor. 4) Repeat this process until there is no longer a common factor.

2

48 7268 12

The product of the factors on the left is the GCF:

2 ● 6 ● 4 = 48

The product of the factors on the left AND bottom is the LCM: 2 ● 6 ● 4 ● 2 ● 3 = 288

42 3

Note that you can pick any common factor to start and any remaining common factor for each step. Try starting by dividing by 3 to see that this is so.

Independent Practice

• Group 1

• Group 2

• Group 3

Quick Quiz

Study Island (Responders)

“Games”

Journal & Summary

• Nine people plan to share equally 24 stamps from one set and 36 stamps from another set. Explain why 9 people cannot share the stamps equally.

• What's is the LCM for two numbers that have no common factors greater than 1? Explain your reasoning.