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Ever wondered how to teach greatest common factors (GCF) and least common multiples (LCM) in an engaging way to your 6th-grade students?

In this lesson plan, students will learn about GCF and LCM and their real-life applications. Through artistic, interactive guided notes, check for understanding, a doodle & color by number activity, and a maze worksheet, students will gain a comprehensive understanding of these important math concepts.

The lesson culminates with a real-life example that explores how GCF and LCM can be applied in practical situations.

- Standard: CCSS 6.NS.B.4
- Topic: Factors, Multiples & Divisibility
- Grades: 5th Grade, 6th Grade
- Type: Lesson Plans

$4.25

After this lesson, students will be able to:

List the factors and multiples of a number

Define and differentiate between greatest common factor (GCF) and least common multiple (LCM)

Identify the GCF and LCM of a set of numbers

Before this lesson, students should be familiar with:

Basic multiplication and division skills of whole numbers

Review of prime and composite numbers

Pencils

Colored pencils or markers

Greatest Common Factor (GCF)

Least Common Multiple (LCM)

Factors

Multiples

As a hook, ask students why understanding greatest common factors (GCF) and least common multiples (LCM) is important in everyday life. You can refer to the real-life application described on the last page of the guided notes, where students read and write about the real-life uses of these math skills.

Use the first page of the guided notes to introduce the topic of factors vs. multiples. Students fill in the guided notes to learn key math vocabulary as well as practice how to find factors and multiples of numbers. Then, use the second page of the guided notes to introduce the greatest common factors (GCF) and least common multiples (LCM). Emphasize that GCF is the largest number that divides evenly into two or more numbers, while LCM is the smallest positive number that is divisible by two or more numbers. It is helpful to walk through the first few examples on the guided notes with your students. Then allow them to practice the rest in groups or independently. Refer to the FAQ below for a walk-through on this, as well as ideas on how to respond to common student questions.

Based on student responses, reteach any concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, while more advanced students begin working on the practice exercises.

Have students practice finding the greatest common factor (GCF) and least common multiple (LCM) using the practice worksheet provided in the resource. This guided notes resource includes a fun maze (page 3) and color by number (page 4) as practice activities for students to work on.

Walk around the classroom to answer any questions students may have while they are working on the practice worksheet.

Use the last page of the guided notes, real life applications, to bring the class back together, and introduce the concept of real-life applications of greatest common factors (GCF) and least common multiples (LCM). The students will read about real life situations where GCF and LCM comes in handy. Then, they will reflect on how GCF and LCM can be used in other real life scenario.

For example, a real-life application of GCF and LCM is in determining the schedule of activities or events. For instance, if you have a set of activities that need to be repeated in a cycle or pattern, finding the LCM will help you determine how long it will take for the activities to align again. This can be particularly useful in planning sports events, music concerts, or other recurring events.

If you’re looking for digital practice for Factors, Multiples, GCF, and LCM, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

Here are 2 activities to explore:

A fun, no-prep way to practice Factors, Multiples, GCF, and LCM is with Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.

Here are 5 activities to try:

A factor is a whole number that can be divided evenly into another number without leaving a remainder. Factors of a number multiplied together will give the original number.

**Some key points about factors:**

Factors are whole numbers.

Factors divide evenly into another number.

Factors can be multiplied together to get the original number.

A multiple is the result of multiplying a number by an integer. In other words, multiples are numbers that can be divided evenly by a given number.

**Some key points about multiples:**

Multiples are generated by multiplying a certain number by different whole numbers.

Multiples are the result of skip counting by a number.

Multiples are always greater than or equal to the original number.

The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers. It is the highest factor that the numbers have in common.

**Some key points about the greatest common factor (GCF):**

The GCF is the largest number that divides evenly into two or more numbers.

The GCF is useful for simplifying fractions and finding the lowest common denominator.

The GCF is used to find the highest common factor between numbers.

To find the greatest common factor (GCF) of two numbers, you can list all the factors of both numbers and find the largest number they have in common. Alternatively, you can use prime factorization to find the GCF.

**Some methods for finding the GCF of two numbers:**

List all factors and identify the largest number they have in common.

Use prime factorization to find the prime factors of both numbers and identify the common prime factors.

The least common multiple (LCM) is the smallest positive number that is divisible by two or more given numbers. It is the smallest common multiple that the numbers share.

**Some key points about the least common multiple (LCM):**

The LCM is the smallest positive number that is divisible by two or more given numbers.

The LCM is used to find the least common denominator in fractions.

The LCM is found by finding the multiples of each number and identifying the smallest common multiple.

To find the least common multiple (LCM) of two numbers, you can list the multiples of both numbers and find the smallest number they have in common. Alternatively, you can use prime factorization to find the LCM.

**Some methods for finding the LCM of two numbers:**

List the multiples of both numbers and identify the smallest number they have in common.

Use prime factorization to find the prime factors of both numbers and identify the common and uncommon prime factors.

The greatest common factor (GCF) and least common multiple (LCM) are related through the fact that the LCM is the product of the GCF and the numbers themselves.

**Key relationship between GCF and LCM:**

The LCM is found by multiplying the GCF of the numbers with the product of the numbers.

The GCF is a factor of both numbers, while the LCM is a multiple of both numbers.

The greatest common factor (GCF) and least common multiple (LCM) are important in various mathematical concepts and problems. They are used in simplifying fractions, adding and subtracting fractions with different denominators, and finding common denominators for rational numbers.

**Importance of GCF and LCM:**

GCF and LCM are essential for simplifying fractions to their lowest terms.

LCM helps find a common denominator for adding and subtracting fractions.

GCF and LCM are used to solve real-life problems involving proportions, ratios, and divisors.

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