Meaning of LCM, HCF and prime numbers and LCM and HCF of two to three 2-digit numbers for Primary 4

Class: Primary 4
Term: First Term
Week: 4
Age: 9 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Number and Numeration
Focal competence: Calculating the LCM and HCF of 2-digit numbers and explaining the meaning of a prime number
Key competencies/values: Collaboration
Skills:

• Generating multiples of numbers
• Generating factors of numbers
• Listing prime numbers

Previous Lesson: Place value of digits and ordering whole numbers
Topic: Whole Numbers: LCM, HCF and Prime Numbers
Subject Matter: Meaning of LCM, HCF and prime numbers, LCM and HCF of two to three 2-digit numbers, meaning/identification of prime numbers, quantitative reasoning

Specific Objectives

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

Cognitive Domain

• Explain the meaning of LCM.
• Explain the meaning of HCF.
• Explain the meaning of a prime number.
• Find the LCM of two to three 2-digit numbers.
• Find the HCF of two to three 2-digit numbers.
• Describe prime numbers.
• Solve problems on quantitative reasoning.

Affective Domain

• Collaborate with peers to solve mathematical problems.
• Appreciate the importance of LCM, HCF, and prime numbers in daily life.

Psychomotor Domain

• List multiples and factors of given numbers accurately.
• Identify prime numbers from a given set 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
• Primary 4 Mathematics Textbook
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Charts showing multiples of numbers
• Charts showing factors of numbers
• Number cards
• Flash cards with prime numbers
• Cardboard for writing numbers

Rationale for the Lesson

This lesson is important as it introduces fundamental concepts in number theory that are essential for higher mathematics. Understanding LCM, HCF, and prime numbers helps pupils develop strong problem-solving skills and provides a foundation for working with fractions, ratios, and algebraic expressions in the future. These concepts also have practical applications in real-life situations, such as scheduling events or dividing items equally.

Prerequisite/Previous Knowledge

Pupils should be able to count numbers, multiply, and divide whole numbers. They should also have a basic understanding of what multiples and factors are.

Lesson Content/Board Summary

Whole Numbers: LCM, HCF and Prime Numbers

Meaning of Least Common Multiple (LCM)

The Least Common Multiple (LCM) of two or more numbers is the smallest non-zero number that is a multiple of all the given numbers. To find the LCM, we list the multiples of each number until we find the first common multiple.

Example of Multiples

Multiples of 6: (6, 12, 18, 24, 30, 36, dots)
Multiples of 8: (8, 16, 24, 32, 40, 48, dots)

Meaning of Highest Common Factor (HCF)

The Highest Common Factor (HCF) of two or more numbers is the largest number that divides exactly into all the given numbers without leaving a remainder. To find the HCF, we list the factors of each number and find the largest factor common to all of them.

Example of Factors

Factors of 12: (1, 2, 3, 4, 6, 12)
Factors of 18: (1, 2, 3, 6, 9, 18)

Meaning of a Prime Number

A prime number is a whole number greater than 1 that has only two factors: 1 and itself. This means it can only be divided exactly by 1 and itself.

Examples of Prime Numbers

Some prime numbers include:

1. 2 (factors: 1, 2)
2. 3 (factors: 1, 3)
3. 5 (factors: 1, 5)
4. 7 (factors: 1, 7)
5. 11 (factors: 1, 11)
6. 13 (factors: 1, 13)

Note: The number 1 is not a prime number because it only has one factor (itself).

Finding LCM of Two 2-Digit Numbers

To find the LCM of two numbers, list their multiples until a common multiple is found.

Example 1: Find the LCM of 12 and 16.

Solution:

Step 1: List the multiples of 12.

(12, 24, 36, 48, 60, 72, dots)

Step 2: List the multiples of 16.

(16, 32, 48, 64, 80, dots)

Step 3: Identify the smallest common multiple.

The smallest number appearing in both lists is 48.

Answer: The LCM of 12 and 16 is (48).

Finding HCF of Two 2-Digit Numbers

To find the HCF of two numbers, list their factors and identify the largest common factor.

Example 1: Find the HCF of 24 and 36.

Solution:

Step 1: List the factors of 24.

(1, 2, 3, 4, 6, 8, 12, 24)

Step 2: List the factors of 36.

(1, 2, 3, 4, 6, 9, 12, 18, 36)

Step 3: Identify the largest common factor.

The largest number appearing in both lists is 12.

Answer: The HCF of 24 and 36 is (12).

Quantitative Reasoning

Quantitative reasoning involves using mathematical concepts to solve real-world problems.

Example 1

Question: Two bells ring at intervals of 10 minutes and 15 minutes respectively. If they both ring together at 9:00 AM, when will they next ring together?

Solution:

Step 1: Understand the problem. We need to find the next time they ring together, which means finding the LCM of their ringing intervals.

Step 2: Find the multiples of 10.

(10, 20, 30, 40, dots)

Step 3: Find the multiples of 15.

(15, 30, 45, 60, dots)

Step 4: Identify the LCM.

The LCM of 10 and 15 is 30.

Step 5: Add the LCM to the starting time.

30 minutes after 9:00 AM is 9:30 AM.

Answer: They will next ring together at 9:30 AM.

Teaching Methods/Instructional Techniques

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

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Activating prior knowledge

Teacher’s Activity: The teacher greets the pupils and asks them to recall what multiples and factors are, giving simple examples. The teacher then introduces the topic of LCM, HCF, and prime numbers.

Pupils’ Activity: Pupils recall and give examples of multiples and factors. They listen attentively to the introduction.

Learning Point: Recall of multiples and factors

Step 2: Explanation of LCM and Multiples

Time: 7 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher explains the meaning of LCM using a chart of multiples. The teacher demonstrates how to list multiples of numbers like 6 and 8 and identify their LCM (e.g., 24).

Pupils’ Activity: Pupils observe the chart, listen to the explanation, and participate in listing multiples.

Learning Point: Meaning of LCM

Step 3: Explanation of HCF and Factors

Time: 7 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher explains the meaning of HCF using a chart of factors. The teacher demonstrates how to list factors of numbers like 12 and 18 and identify their HCF (e.g., 6).

Pupils’ Activity: Pupils observe the chart, listen to the explanation, and participate in listing factors.

Learning Point: Meaning of HCF

Step 4: Explanation of Prime Numbers

Time: 6 minutes

Teaching Skill: Explanation/Identification

Teacher’s Activity: The teacher explains what a prime number is, emphasising that it has only two factors: 1 and itself. The teacher uses flashcards to show examples of prime numbers like 2, 3, 5, 7, 11.

Pupils’ Activity: Pupils listen, identify prime numbers on flashcards, and ask questions for clarification.

Learning Point: Definition of prime number

Step 5: Guided Practice on LCM and HCF Calculation

Time: 7 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher guides pupils through finding the LCM of two 2-digit numbers (e.g., 12 and 16) and the HCF of two 2-digit numbers (e.g., 24 and 36) on the board, following the steps outlined in the Board Summary.

Pupils’ Activity: Pupils follow along, contribute to listing multiples/factors, and work out the LCM and HCF with the teacher’s guidance.

Learning Point: Calculating LCM and HCF

Step 6: Quantitative Reasoning Application

Time: 4 minutes

Teaching Skill: Problem Solving

Teacher’s Activity: The teacher presents a simple quantitative reasoning problem (e.g., the bell ringing problem) and guides pupils to identify whether LCM or HCF is needed to solve it. The teacher then guides them through the solution.

Pupils’ Activity: Pupils analyse the problem, suggest approaches, and participate in solving it.

Learning Point: Applying LCM/HCF to problems

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 the meaning of LCM?
2. What is the meaning of HCF?
3. Give two examples of prime numbers.
4. Find the LCM of 10 and 15.
5. Find the HCF of 20 and 30.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Understanding LCM, HCF, Prime Numbers

Step 8: Note-Taking

Time: 4 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils to copy the essential Board Summary notes into their notebooks, focusing on definitions and worked examples.

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

Learning Point: Recording lesson content

Step 9: Conclusion

Time: 1 minute

Teaching Skill: Consolidation

Teacher’s Activity: The teacher briefly summarises the main points of the lesson, reinforcing the importance of LCM, HCF, and prime numbers. The teacher encourages pupils to practice more examples at home.

Pupils’ Activity: Pupils listen and prepare for the next activity.

Learning Point: Lesson summary and reinforcement

Continuous Assessment/Further Study

Type: Homework

Instruction: Solve the following problems in your mathematics notebook.

1. Explain in your own words what a prime number is.
2. List all the factors of 28.
3. List the first five multiples of 9.
4. Find the LCM of 8 and 12.
5. Find the HCF of 18 and 27.

Lesson Keywords

• Multiple – The result of multiplying a number by an integer.
• Factor – A number that divides another number exactly without leaving a remainder.
• Prime Number – A whole number greater than 1 that has only two factors: 1 and itself.
• LCM (Least Common Multiple) – The smallest common multiple of two or more numbers.
• HCF (Highest Common Factor) – The largest common factor of two or more numbers.

Differentiation

Support for weaker learners: Provide additional charts with pre-listed multiples and factors. Offer one-on-one guidance during practice sessions and simplify the numbers used in examples. Focus on understanding definitions before calculations.

Extension for faster learners: Challenge them to find the LCM and HCF of three 2-digit numbers or larger numbers. Introduce the prime factorization method for finding LCM and HCF as an advanced concept.

Suggested Lesson Videos

Search YouTube for: “Primary 4 LCM HCF Prime Numbers Nigeria”

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure you have prepared all instructional materials, especially the charts for multiples, factors, and prime numbers. Begin by reviewing prior knowledge of multiples and factors to ensure a smooth transition into the new concepts. Clearly explain the definitions of LCM, HCF, and prime numbers, using visual aids to make the concepts concrete. Guide pupils through step-by-step calculations for LCM and HCF using the listing method, allowing them to actively participate. Encourage collaboration during problem-solving activities. During the note-taking stage (Step 8), ensure pupils copy the Board Summary accurately. Pay attention to common errors, such as confusing multiples with factors or misunderstanding the definition of a prime number. Provide individual support where needed and challenge faster learners with more complex problems. Conclude by reinforcing the key learning points and assigning relevant homework for continuous practice.