Mastering Least Common Multiple with Variables

Algebra 2 Grades High School 4:04 Video
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Lesson Description

Learn to find the Least Common Multiple (LCM) with variables, including monomials, binomials, and trinomials. This lesson covers prime factorization and factoring techniques to determine the LCM effectively.

Video Resource

Finding a Least Common Multiple (With Variables)

Mario's Math Tutoring

Duration: 4:04
Watch on YouTube

Key Concepts

  • Prime Factorization
  • Least Common Multiple (LCM)
  • Factoring Polynomials

Learning Objectives

  • Students will be able to find the prime factorization of integers and algebraic expressions.
  • Students will be able to determine the Least Common Multiple (LCM) of monomials, binomials, and trinomials.
  • Students will be able to apply LCM to find common denominators when working with rational expressions.

Educator Instructions

  • Introduction (5 mins)
    Begin with a brief review of finding the LCM of integers. Explain the connection to finding common denominators in fractions. Introduce the concept of extending this to algebraic expressions and the importance of factoring.
  • Prime Factorization of Numbers (10 mins)
    Review how to find the prime factorization of a number, as shown at the beginning of the video. Example: Finding prime factors of 14 and 20. Emphasize writing the prime factorization in exponential notation.
  • LCM with Monomials (15 mins)
    Work through Example 1 from the video: Finding the LCM of 8x²y³ and 20xy⁵. Clearly demonstrate how to factor the coefficients and identify the highest power of each variable. Step-by-step instructions on how to handle both coefficients and variable exponents.
  • LCM with Binomials and Trinomials (20 mins)
    Address Example 2 from the video: Finding the LCM of x² - 9 and x² - x - 12. Guide students through factoring the difference of squares and the trinomial. Explain the importance of factoring before determining the LCM. Emphasize the concept of taking the factor that occurs the most.
  • Practice Problems (15 mins)
    Provide students with practice problems of varying difficulty levels. Include both monomial and polynomial examples. Circulate to provide assistance and answer questions.
  • Wrap-up and Extension (5 mins)
    Summarize the key concepts of the lesson. Briefly discuss how finding the LCM is used when adding or subtracting rational expressions. Refer students to additional resources and practice problems.

Interactive Exercises

  • Factorization Challenge
    Students are given various polynomials to factor. The first student to correctly factor each polynomial wins a small prize.
  • LCM Relay Race
    Divide students into teams. Each team receives a set of expressions, and each member must find the LCM of a different set of expressions. The first team to correctly solve all problems wins.

Discussion Questions

  • Why is prime factorization important when finding the LCM?
  • What is the difference between finding the Greatest Common Factor (GCF) and the Least Common Multiple (LCM)?
  • How can finding the LCM help simplify rational expressions?

Skills Developed

  • Factoring Polynomials
  • Identifying Prime Factors
  • Problem-Solving

Multiple Choice Questions

Question 1:

What is the first step in finding the LCM of two polynomials?

Correct Answer: Factor each polynomial

Question 2:

What is the LCM of 12x³y² and 18xy⁴?

Correct Answer: 36x³y⁴

Question 3:

The LCM of (x + 2) and (x - 2) is:

Correct Answer: x² - 4

Question 4:

What is the LCM of x² - 4 and x + 2?

Correct Answer: x² - 4

Question 5:

Which of the following is the correct prime factorization of 36?

Correct Answer: 2² x 3²

Question 6:

The LCM of two expressions will always be...

Correct Answer: Divisible by both expressions

Question 7:

What should you do if you have the same factor in both expressions?

Correct Answer: Choose the one with the larger exponent

Question 8:

The LCM of x² + 5x + 6 and x² + 6x + 9 is:

Correct Answer: (x+2)(x+3)²

Question 9:

Finding the LCM is most helpful when:

Correct Answer: Adding fractions with unlike denominators

Question 10:

The LCM of x, x+1, and x-1 is:

Correct Answer: x(x²-1)

Fill in the Blank Questions

Question 1:

The first step to finding the LCM of polynomials is to __________ each polynomial.

Correct Answer: factor

Question 2:

The LCM of 5x² and 10x³ is __________.

Correct Answer: 10x³

Question 3:

x² - 9 can be factored as (x + 3)(__________)

Correct Answer: x - 3

Question 4:

The LCM of (x + 1) and (x + 2) is (x + 1)(__________)

Correct Answer: x + 2

Question 5:

When finding the LCM, you take the factor that occurs ___________.

Correct Answer: most

Question 6:

The prime factorization of 28 is 2² * ___________.

Correct Answer: 7

Question 7:

LCM stands for ___________ Common Multiple.

Correct Answer: Least

Question 8:

Finding the LCM helps in simplifying _______ expressions.

Correct Answer: rational

Question 9:

To factor x² + 5x + 6, you need two numbers that multiply to 6 and add to ___________.

Correct Answer: 5

Question 10:

If a term is present in one expression, but not the other, you ___________ include it in the LCM.

Correct Answer: still

Educational Standards

A2.A.2.1:Factor polynomial expressions including, but not limited to, trinomials, differences of squares, sum and difference of cubes, and factoring by grouping, using a variety of tools and strategies. A2.A.2.3:Add, subtract, multiply, divide, and simplify rational expressions.

Teaching Materials

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