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## Finding GCF’s and LCM’s

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**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**• 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 We are looking for a factor. The factor must be common to both numbers. We need to pick the greatest of such common factors.**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**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:**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.**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**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.**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**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.