Meaning of Lowest Common Multiple (LCM) and Multiple of whole numbers for JSS 1

Class: JSS 1
Term: First Term
Week: 4
Age: 12 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: NUMBER NUMERATION
Focal competence: Calculate the LCM of two or more whole numbers
Key competencies/values: Collaboration; Critical Thinking
Skills:

• Determining of common multiples of two or more whole numbers

Previous Lesson: Meaning of a multiple and a common multiple
Topic: Lowest Common Multiples (LCM): Lowest Common Multiple (LCM)
Subject Matter: Meaning of Lowest Common Multiple (LCM), Multiple of whole numbers, LCM of whole numbers

Specific Objectives

By the end of the lesson, pupils/students should be able to:

Cognitive Domain

• Define Lowest Common Multiple (LCM).
• Identify multiples and common multiples of two or more whole numbers.
• Determine common multiples of whole numbers.
• Find the LCM of two or more whole numbers using the listing method.
• Find the LCM of given numbers using the index method.

Affective Domain

• Appreciate the importance of LCM in solving real-life problems.
• Collaborate effectively with peers during group activities.

Psychomotor Domain

• Accurately list multiples of given numbers.
• Correctly apply the index method to find the LCM of numbers.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• New General Mathematics for Junior Secondary Schools 1
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Place value Number Charts
• Flash cards
• Number cards
• Venn diagram on multiples of two or more numbers

Rationale for the Lesson

Understanding LCM is fundamental in mathematics, especially for operations involving fractions with different denominators. It helps students develop critical thinking skills and forms a basis for more advanced number theory concepts. This lesson provides practical methods for calculating LCM, which is applicable in various real-world scenarios.

Prerequisite/Previous Knowledge

Students should have prior knowledge of multiplication tables, factors of whole numbers, and prime numbers.

Lesson Content/Board Summary

Lowest Common Multiples (LCM)

Multiples of Whole Numbers

A multiple of a whole number is the result of multiplying that number by any other whole number (except zero). In other words, multiples are the numbers you get when you count by a certain number.

Multiples can be generated by repeated addition or multiplication.

For example, the multiples of 3 are:

1. (3 times 1 = 3)
2. (3 times 2 = 6)
3. (3 times 3 = 9)
4. (3 times 4 = 12)
5. (3 times 5 = 15)
6. … and so on.

So, the multiples of 3 are (3, 6, 9, 12, 15, 18, ldots).

The multiples of 4 are (4, 8, 12, 16, 20, 24, ldots).

Common Multiples

Common multiples are the multiples that two or more numbers share. They appear in the list of multiples for each number.

For example, let’s find the common multiples of 3 and 4:

Multiples of 3: (3, 6, 9, textbf{12}, 15, 18, 21, textbf{24}, 27, 30, 33, textbf{36}, ldots)

Multiples of 4: (4, 8, textbf{12}, 16, 20, textbf{24}, 28, 32, textbf{36}, 40, ldots)

The common multiples of 3 and 4 are (12, 24, 36, ldots).

Lowest Common Multiple (LCM)

The Lowest Common Multiple (LCM) of two or more whole numbers is the smallest non-zero common multiple among them.

Finding LCM by Listing Multiples

This method involves listing the multiples of each number until the first common multiple is found.

Steps:

1. List the multiples of each given number.
2. Identify the common multiples from the lists.
3. The smallest common multiple is the LCM.

Example 1

Question: Find the LCM of 6 and 8.

Solution:

Multiples of 6: (6, 12, 18, textbf{24}, 30, 36, 42, textbf{48}, ldots)

Multiples of 8: (8, 16, textbf{24}, 32, 40, textbf{48}, 56, ldots)

The common multiples are (24, 48, ldots).

The lowest (smallest) common multiple is 24.

Answer: The LCM of 6 and 8 is 24.

Finding LCM by Prime Factorization (Index Method)

This method involves expressing each number as a product of its prime factors in index form.

Steps:

1. Find the prime factorization of each number.
2. Express each prime factorization in index form.
3. Identify all distinct prime factors that appear in any of the factorizations.
4. For each distinct prime factor, take the highest power (exponent) it appears with in any of the factorizations.
5. Multiply these highest powers together to get the LCM.

Example 2

Question: Find the LCM of 12 and 18 using the prime factorization method.

Solution:

Step 1: Find the prime factors of each number.

(12 = 2 times 2 times 3)

(18 = 2 times 3 times 3)

Step 2: Express in index form.

(12 = 2^2 times 3^1)

(18 = 2^1 times 3^2)

Step 3: Identify distinct prime factors and their highest powers.

Distinct prime factors are 2 and 3.

Highest power of 2 is (2^2) (from 12).

Highest power of 3 is (3^2) (from 18).

Step 4: Multiply the highest powers.

(LCM = 2^2 times 3^2 = 4 times 9 = 36)

Answer: The LCM of 12 and 18 is 36.

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Individual Practice, Pair Work

Instructional Procedures

Step 1: Introduction

Time: 3 minutes

Teaching Skill: Activating prior knowledge

Teacher’s Activity: The teacher greets the students and asks them to state the multiplication table of 2 and 3 orally. The teacher also asks students to recall what a factor is.

Pupils’ Activity: Students respond by reciting multiplication tables and recalling the definition of a factor.

Learning Point: Recalling multiplication facts

Step 2: Meaning of Multiples

Time: 6 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher explains the meaning of a multiple of a whole number, demonstrating how to generate multiples using repeated addition and multiplication with examples like 3 and 5. The teacher uses a number chart to highlight multiples.

Pupils’ Activity: Students listen attentively, observe the number chart, and participate by suggesting the next multiples.

Learning Point: Definition of a multiple

Step 3: Listing Multiples

Time: 6 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher guides students to list the first few multiples of given numbers (e.g., 4, 7) on the board. The teacher uses flashcards with numbers to prompt students.

Pupils’ Activity: Students actively list multiples in their notebooks and on the board, checking their answers.

Learning Point: Generating number multiples

Step 4: Common Multiples

Time: 6 minutes

Teaching Skill: Explanation/Identification

Teacher’s Activity: The teacher explains what common multiples are by listing multiples of two numbers (e.g., 2 and 3) and circling the numbers that appear in both lists. A Venn diagram is used to illustrate overlapping multiples.

Pupils’ Activity: Students identify the common multiples from the lists and observe the Venn diagram.

Learning Point: Identifying common multiples

Step 5: Lowest Common Multiple (LCM) by Listing

Time: 6 minutes

Teaching Skill: Demonstration/Problem Solving

Teacher’s Activity: The teacher defines LCM as the smallest common multiple. Using the previous example of common multiples (e.g., 2 and 3), the teacher guides students to identify the LCM. The teacher works through Example 1 from the Board Summary (LCM of 6 and 8) with the class.

Pupils’ Activity: Students define LCM and follow the steps to find the LCM of given numbers by listing multiples.

Learning Point: Finding LCM by listing

Step 6: Finding LCM by Prime Factorization (Index Method)

Time: 7 minutes

Teaching Skill: Explanation/Application

Teacher’s Activity: The teacher introduces the prime factorization method for finding LCM, reviewing prime numbers and index form. The teacher demonstrates the steps using Example 2 from the Board Summary (LCM of 12 and 18), ensuring students understand how to select the highest powers of prime factors.

Pupils’ Activity: Students listen, ask questions, and practice finding prime factors and applying the index method to find LCM.

Learning Point: LCM using index method

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is a multiple of a number?
2. List the first five multiples of 9.
3. What are common multiples?
4. Find the LCM of 4 and 6 by listing their multiples.
5. Determine the LCM of 15 and 20 using the prime factorization method.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Understanding LCM concepts

Step 8: Note-Taking

Time: 4 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes on the meaning of multiples, common multiples, LCM, and the two methods of finding LCM into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Recording lesson notes

Step 9: Conclusion

Time: 2 minutes

Teaching Skill: Summarization

Teacher’s Activity: The teacher briefly summarizes the key concepts of multiples, common multiples, and LCM, emphasizing the two methods taught. The teacher encourages students to practice more examples at home.

Pupils’ Activity: Students listen and ask any final clarifying questions.

Learning Point: Consolidating LCM knowledge

Continuous Assessment/Further Study

Type: Homework

Instruction: Solve the following problems in your mathematics notebook.

1. List the first six multiples of 7.
2. Find the common multiples of 5 and 10 up to 50.
3. What is the LCM of 9 and 12 using the listing method?
4. Use the prime factorization method to find the LCM of 24 and 36.
5. Explain in your own words why finding the LCM is useful.

Lesson Keywords

• Multiple – The result of multiplying a number by an integer.
• Common Multiple – A number that is a multiple of two or more numbers.
• Lowest Common Multiple (LCM) – The smallest non-zero common multiple of two or more numbers.
• Prime Factorization – Expressing a number as a product of its prime factors.
• Index Form – Writing a number using powers (exponents).

Differentiation

For students who struggle, provide a multiplication chart and work through additional simple examples using the listing method. For advanced learners, challenge them to find the LCM of three numbers or explore real-life problems where LCM is applied, such as scheduling events or packaging items.

Suggested Lesson Videos

Search YouTube for “Lowest Common Multiple JSS 1” or “How to find LCM of numbers”.

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure all instructional materials, especially the number chart, flashcards, and a pre-drawn Venn diagram (or materials to draw one), are ready. Begin by reviewing multiplication facts to ensure students have the prerequisite knowledge. Present the concepts of multiples and common multiples clearly before introducing LCM. Demonstrate both the listing and prime factorization methods with clear, step-by-step examples. Encourage student participation through questioning and guided practice. During Step 8, guide students to copy the Board Summary notes accurately into their notebooks, emphasizing clarity and organization. Pay close attention to students’ understanding of prime factorization, as it is key to the index method. Provide extra support for students who find prime factorization challenging and offer extension tasks for those who grasp the concepts quickly. Ensure all students can define and calculate LCM using at least one method by the end of the lesson.