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Notes 9/9/10 Prime Time Definitions Greatest Common Factor (GCF): The greatest factor that two (or more!) numbers share. Ex: The GCF for 36 and 24 is 12. Least Common Multiple (LCM): The smallest number that is a multiple of two numbers. Ex: 12 is the LCM of 3 and 4.

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Greatest Common Factor 1)Find the Prime Factorization 2)Put the results in a Venn Diagram 3) The shared numbers go in the shared space (middle) of the Venn Diagram 4) Multiply the shared number together = GCF

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Factors of 56 What is the GCF for these two numbers? _______ Factors of 56 Factors of 28 The numbers that are the same Leftover numbers

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Factors of 28Factors of 56 What is the GCF for these two numbers? _______ Factors of 56Factors of 28

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GCF Practice Find the GCF for the following numbers (use a Venn Diagram) - 24 and 30 –15 and 60 –30 and 50

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Least Common Multiple 1) Find the GCF 2) Place the leftover numbers (ones not shared) in the Venn Diagram. 3) Multiply all numbers in the Venn Diagram = LCM

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LCM Practice Leftover numbers go here 20 50 Leftover numbers go here GCF What is the LCM for these two numbers? _______

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LCM Practice Find the LCM of these two numbers: 5 and 7 10 and 15

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REAL LIFE PROBLEM SOLVING USING GCF AND LCM You have 27 Reese’s Cups and 66 M & M’s. Including yourself, what is the greatest number of friends you can enjoy your candy with so that everyone gets the same amount?

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REAL LIFE PROBLEM SOLVING USING GCF AND LCM Molly’s uncle donated 100 cans of juice and 20 packs of cheese crackers for the school picnic. Each student is to receive the same number of cans of juice and the same number of packs of crackers. What is the largest number of students that can come to the picnic and share the food equally? How many cans of juice and how many packs of crackers will each student receive?

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REAL LIFE PROBLEM SOLVING USING GCF AND LCM Mrs. McCrary and 23 of her students are planning to eat hot dogs at the upcoming DMS picnic. Hot dogs come in packages of 12 and buns come in packages of 8. What is the smallest number of packs of dogs and the smallest number of packs of buns Mrs. McCrary can buy so that everyone INCLUDING HER can have the same number of hot dogs and there are no leftovers? How many dogs and buns does each person get?

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Greatest Common Factor and Least Common Multiples GCF and LCM

Greatest Common Factor and Least Common Multiples GCF and LCM

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