Unlocking the Magic of Least Common Multiple (LCM)

Mathematics Grades 4th Grade 5:40 Video
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Lesson Description

Learn how to find the Least Common Multiple (LCM) of two numbers using different methods, including listing multiples and prime factorization. Discover how LCM helps with fractions!

Video Resource

Least Common Multiple (LCM)

Professor Dave Explains

Duration: 5:40
Watch on YouTube

Key Concepts

  • Multiples
  • Common Multiples
  • Least Common Multiple (LCM)
  • Prime Factorization
  • Fractions and Common Denominators

Learning Objectives

  • Students will be able to define multiples and identify multiples of a given number.
  • Students will be able to find the Least Common Multiple (LCM) of two numbers by listing multiples.
  • Students will be able to find the Least Common Multiple (LCM) of two numbers using prime factorization.
  • Students will be able to explain how LCM is used to find common denominators for fractions.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what they know about multiples. Briefly review multiplication facts. Introduce the concept of comparing numbers and finding common ground, leading into the idea of common multiples.
  • Video Viewing (7 mins)
    Play the Professor Dave Explains video on Least Common Multiple (LCM). Encourage students to take notes on key terms and methods.
  • Listing Multiples (10 mins)
    Work through examples of finding the LCM by listing multiples. Start with small numbers (e.g., 2 and 3, 4 and 6) and gradually increase the difficulty. Have students work independently or in pairs to practice.
  • Prime Factorization Method (15 mins)
    Introduce the prime factorization method for finding the LCM. Explain how to find the prime factors of each number. Demonstrate how to identify the highest power of each prime factor and multiply them together to find the LCM. Provide practice problems for students to solve.
  • LCM and Fractions (8 mins)
    Explain how the LCM is used to find a common denominator when adding or subtracting fractions. Work through examples, showing how to convert fractions to equivalent fractions with the common denominator. Remind students that the video touches on this concept.

Interactive Exercises

  • Multiple Mania
    Write a number on the board (e.g., 6). Have students take turns calling out multiples of that number. Continue until they reach a certain number (e.g., 60) or until someone makes a mistake.
  • LCM Scavenger Hunt
    Divide students into small groups. Give each group a set of number pairs. Have them find the LCM of each pair using either the listing multiples method or the prime factorization method. The first group to correctly find all the LCMs wins.

Discussion Questions

  • What is a multiple?
  • What is a common multiple?
  • What is the difference between a common multiple and the Least Common Multiple (LCM)?
  • How can finding the LCM help us with fractions?

Skills Developed

  • Multiplication
  • Problem-solving
  • Critical thinking
  • Prime Factorization
  • Comparing numbers

Multiple Choice Questions

Question 1:

What is a multiple of a number?

Correct Answer: A number you get when you multiply.

Question 2:

Which of these is a multiple of 7?

Correct Answer: 14

Question 3:

What is the Least Common Multiple (LCM) of 2 and 3?

Correct Answer: 6

Question 4:

What is a factor of a number?

Correct Answer: A number that is multiplied by another number to find a product.

Question 5:

Which of the following is NOT a multiple of 5?

Correct Answer: 22

Question 6:

Which method can be used to find the LCM?

Correct Answer: Both A and B

Question 7:

Why is LCM useful when working with fractions?

Correct Answer: To find a common denominator.

Question 8:

What are the prime factors of 12?

Correct Answer: 2 x 2 x 3

Question 9:

What is the LCM of 4 and 5?

Correct Answer: 20

Question 10:

Which is the best way to find the LCM of big numbers?

Correct Answer: Prime factorization.

Fill in the Blank Questions

Question 1:

A ________ is a number you get when you multiply a number by a whole number.

Correct Answer: multiple

Question 2:

The smallest multiple that two numbers share is called the ________.

Correct Answer: LCM

Question 3:

To find the LCM of 6 and 8, you can list the ________ of each number.

Correct Answer: multiples

Question 4:

Another way to find the LCM is by using ________ ________.

Correct Answer: prime factorization

Question 5:

The LCM of 3 and 4 is ________.

Correct Answer: 12

Question 6:

We use the LCM to find a common ________ when adding or subtracting fractions.

Correct Answer: denominator

Question 7:

A ________ number can only be divided by itself and 1.

Correct Answer: prime

Question 8:

The prime factors of 10 are 2 and ________.

Correct Answer: 5

Question 9:

When finding the LCM using prime factorization, we take the ________ power of each prime factor.

Correct Answer: highest

Question 10:

If the LCM of two numbers is the same as their product, they have no common ________ other than 1.

Correct Answer: factors

Educational Standards

4.N.2.1:Demonstrate fluency with multiplication and division facts with factors up to 12. 4.N.3.5:Use models to add and subtract fractions with like denominators. 4.N.1.1:Read, write, discuss, and represent whole numbers up to 1,000,000. Representations may include numerals, words, pictures, number lines, and manipulatives.

Teaching Materials

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