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**Prime Time Investigation 3**

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**Let’s Review Vocabulary**

Multiple Common Multiple Factor Common Factor Greatest Common Factor

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**What are the first ten multiples of 20? Of 30?**

What numbers (multiples) occur on both lists? We call these common multiples. What do these numbers have in common? What is the least number that occurs on both lists? This number is called the least common multiple of 20 and 30. Let’s define Least Common Multiple in our notebooks.

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**The least multiple that two or more numbers share.**

Least Common Multiple The least multiple that two or more numbers share. Ex: 6 = 6, 12, 18, 24, 30, 36, 42, 48 8 = 8, 16, 24, 32, 40, 48 SO – common multiples are 24 & 48 The LCM is 24

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Common Factors What are the factors of 12? Of 30? What numbers occur on both lists? We call these common factors. What properties do these numbers have in common? What is the greatest number on the list? This number is called the greatest common factor. Let’s define greatest common factor in our notebooks.

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**Greatest Common Factor (GCF)**

The greatest number that is a factor of each or two or more numbers. The factors of 12 are = 1, 2, 3, 4, 6, 12 The factors of 18 are = 1, 2, 3, 6, 9, 18 The greatest common factor is 6.

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**Ferris wheel How many of you have ever been on a Ferris wheel?**

How many trips around do you get? How does the size of the wheel affect your ride? Today we’re going to be solving a problem about a Ferris wheel ride.

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**Investigation 3.1 Closing**

Switch partners with someone and use the P.A.L. strategy to discuss the problem. Did you like using P.A.L? In your own words in you notebook, write about how finding common multiples helped you solve the Ferris wheel problem.

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Investigation 3.2 Today, we are going to look at another situation that considers when two or more things will happen again at the same time. Your challenge is to find when two types of cicadas will appear at the same time.

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CiCadas Cicadas spend most of their lives underground. Some populations of cicadas come above ground every 13 years, while others come up every 17 years. Although cicadas do not cause damage directly to fruits and vegetables, they can damage orchards because the female makes slits in trees to lay her eggs. We are about to solve a problem about cicadas. You will be doing your work in your journal, but be prepared to share what your group has done in your notebook on the ELMO with the class.

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**Your Challenge Problem**

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**Let’s share our solutions:**

** Remember to explain your strategies for solving as well as your solution when you share. Journal Response: How can we tell when the least common multiple will be the product or the two numbers given, and when the least common multiple will be less than the product of the two numbers?

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WARM UP Find the greatest common factor (GCF): 1.24, 30, 42 Find the least common multiple (LCM): 1.4, 12, 16.

WARM UP Find the greatest common factor (GCF): 1.24, 30, 42 Find the least common multiple (LCM): 1.4, 12, 16.

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