Multi-Digit and Fraction Computation

Lesson 17

Objective

Solve mathematical and real-world problems using the greatest common factor and least common multiple. 

Common Core Standards

Core Standards

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  • 6.NS.B.4 — Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

Foundational Standards

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  • 4.OA.B.4

Criteria for Success

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  1. Find two numbers when given information about them, including their greatest common factor and least common multiple.
  2. Express a sum of two whole numbers with a common factor as a multiple of a sum of two relatively prime numbers. For example, express 36 + 8 as 4(9 + 2).
  3. Determine if a problem can be solved by finding the greatest common factor or the least common multiple. 
  4. Solve real-world problems that involve finding the greatest common factor or the least common multiple.

Tips for Teachers

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Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Problems

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Problem 1

Two numbers can be described with the information below:

  • Both numbers are less than 20.
  • The greatest common factor of the two numbers is 2.
  • The least common multiple of the two numbers is 36.

What are the two numbers?

Guiding Questions

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Problem 2

Jason is preparing bundles of markers and pencils for a class activity. He wants to make the greatest number of bundles that he can, with the same number of markers and pencils in each bundle. Jason has 15 markers and 35 pencils. He writes the following equation to help him make sense of his supplies:

$${15+35=5(3+7)}$$

  1. What does Jason’s equation tell him about how many bundles he can make and how many markers and pencils are in each bundle?

 

  1. Mai, in another class, is also preparing bundles of markers and pencils. She has 24 markers and 36 pencils. She writes an equation and determines that she can make at most 4 bundles. Do you agree with Mai’s reasoning? Explain. 

$${24+36=4(6+9)}$$

  1. If you have 18 markers and 48 pencils, what is the greatest number of bundles you can make? How many markers and pencils in each bundle? Write an equation to represent this. 

Guiding Questions

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Problem 3

The florist can order roses in bunches of one dozen and lilies in bunches of 8. Last month she ordered the same number of roses as lilies. If she ordered no more than 100 roses, how many bunches of each could she have ordered? What is the smallest number of bunches of each that she could have ordered? Explain your reasoning.

Guiding Questions

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References

Illustrative Mathematics The Florist Shop

The Florist Shop, accessed on Sept. 28, 2017, 4:42 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem Set

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With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Include a mix of GCF and LCM word problems; a simple search for this should generate several resources on the Internet.

Target Task

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Problem 1

Two numbers less than 25 have a least common multiple of 60 and a greatest common factor of 5. What are the two numbers?

Problem 2

Find the greatest common factor of the two numbers below and rewrite the sum using the distributive property.

$${20 + 36}$$

Mastery Response

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