Curriculum / Math / 6th Grade / Unit 3: Multi-Digit and Fraction Computation / Lesson 16
Math
Unit 3
6th Grade
Lesson 16 of 17
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Find the least common multiple of two numbers. Solve application problems using the least common multiple.
The core standards covered in this lesson
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).
The foundational standards covered in this lesson
4.OA.B.4 — Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
a. List all the multiples of 8 that are less than or equal to 100.
b. List all the multiples of 12 that are less than or equal to 100.
c. What are the common multiples of 8 and 12 from the two lists?
d. What is the least common multiple of 8 and 12?
e. Lyle noticed that the list of common multiples has a pattern. Describe a pattern in the list of numbers that Lyle might have seen.
Multiples and Common Multiples, accessed on Sept. 28, 2017, 4:34 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.
a. Find the least common multiple of 8 and 12 using prime factorization.
b. Use this same method to find the least common multiple of 12 and 9.
Tre has two alarm clocks set to go off in the morning. One alarm will buzz every 6 minutes, and the other will beep every 9 minutes. Both alarms go off at 6:15 a.m.
Tre thinks the next time that both alarms will go off at the same time will be in 54 minutes or at 7:09. Do you agree with Tre? Explain your reasoning.
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Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
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Find the least common multiple of 6 and 14. Show your work.
A Venn diagram showing the prime factors for two numbers is shown below. Use it to answer the questions.
a. What two numbers are represented in the diagram?
b. What is the greatest common factor of the two numbers?
c. What is the least common multiple of the two numbers?
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The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 15
Lesson 17
Topic A: Dividing with Fractions
Interpret division problems as the number of items in each group or the number of groups of a given number of items. Write corresponding multiplication and division problems.
6.NS.A.1
Divide a fraction by a whole number using visual models and related multiplication problems.
Divide a whole number by a fraction using visual models.
Use visual models and patterns to develop a general rule to divide with fractions.
Solve and write story problems involving division with fractions.
Solve problems involving division with fractions.
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Topic B: Computing with Decimals
Add and subtract decimals using the standard algorithm.
6.NS.B.3
Multiply decimals using strategies, and develop an understanding of the standard algorithm.
Multiply decimals using the standard algorithm.
Divide multi-digit whole numbers using the standard algorithm.
6.NS.B.2
Divide numbers with decimal quotients. Divide decimals by whole numbers.
6.NS.B.2 6.NS.B.3
Divide decimals by decimals using the standard algorithm.
Solve problems involving decimals using all four operations.
Topic C: Applying the Greatest Common Factor and the Least Common Multiple
Use prime factorization to represent numbers as products of prime factors.
6.NS.B.4
Find the greatest common factor of two numbers. Solve application problems using the greatest common factor.
Solve mathematical and real-world problems using the greatest common factor and least common multiple.
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