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# Finding GCF’s and LCM’s

Finding GCF’s and LCM’s. Grade 6. Learning Objective. I can: 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. Vocabulary.

## Finding GCF’s and LCM’s

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1. Finding GCF’s and LCM’s Grade 6

2. Learning Objective I can: 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.

3. 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.

4. Finding the Greatest Common Factor of Two Numbers We are looking for a factor. The factor must be common to both numbers. We need to pick the greatest of such common factors.

5. The GCF of 36 and 90 Method 1 1) List the factors of each number. 36: 1 2 3 4 6 36 18 24 9 90: 1 2 3 5 6 9 90 45 30 18 15 10 2) Circle the common factors. 3) The greatest of these will be your Greatest Common Factor: 18

6. The GCF of 36 and 90 Method 2 1) Prime factor each number. 36 = 2 ● 2 ● 3 ●3 90 = 2 ● 3 ● 3 ●5 2) Circle each pair of common prime factors. 3) The product of these common prime factors will be 2 ● 3 ● 3 =18 the Greatest Common Factor:

7. Finding the Least Common Multiple of Two Numbers We are looking for a multiple. The multiple must be common to both numbers. We need to pick the least of such common multiples.

8. The LCM of 12 and 15 Method 1 1) List the first few multiples of each number. 12: 12 24 36 48 60 72 84 90 108 120 15: 15 30 45 60 75 90 105 120 135 2) Circle the common multiples. 3) The least of these will be your Least Common Multiple: 60

9. The LCM of 12 and 15. Method 2 1) Prime factor each number. 12 = 2 ● 2 ● 3 15 = 5 ● 3 2) Circle each pair of common prime factors. 3) Circle each remaining prime factor. 4) Multiply together one factor from each circle to get the 3 ● 2 ● 2 ● 5=60 Least Common Multiple : Note that the common factor, 3, was only used once.

10. Method 3: Find both GCF and LCM at Once. The GCF and LCM of 72 and 90 1) Make the following table. 9 8 2 10 4 5 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. The product of the factors on the left is the GCF: The product of the factors on the left AND bottom is the LCM: 9 ● 2= 18 9 ● 2● 4● 5 = 360

11. 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.

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