Mathematics - Junior Secondary 1 - Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of Whole Numbers

Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of Whole Numbers

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TERM: 1ST TERM

WEEK 3

Class: Junior Secondary School 1
Age: 12 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of Whole Numbers
Focus: Concepts, Inspection, Formulae, Application

SPECIFIC OBJECTIVES:

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

  1. Explain the concepts of LCM and HCF.
  2. Find LCM and HCF of given numbers by inspection.
  3. Use formulae to find LCM and HCF.
  4. Solve word problems involving LCM and HCF.
  5. Apply LCM and HCF in quantitative reasoning tasks.

INSTRUCTIONAL TECHNIQUES:

  • Explanation
  • Question and answer
  • Group exercises
  • Guided practice
  • Real-life word problems

INSTRUCTIONAL MATERIALS:

  • Multiplication charts
  • Flashcards
  • Worksheets
  • Whiteboard and marker
  • Number tiles
  • Quantitative reasoning textbook

 

PERIOD 1 & 2: Concepts of LCM and HCF

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces LCM and HCF using everyday examples (e.g. grouping, common schedules).

Pupils listen and contribute examples.

Step 2 - Explanation

Explains that LCM is the smallest common multiple, HCF is the greatest common factor.

Pupils repeat and take notes.

Step 3 - Demonstration

Uses small numbers (e.g. 4 and 6) to show multiples and common factors.

Pupils find LCM and HCF with guidance.

Step 4 - Note Taking

Writes summary on board, pupils copy.

Pupils copy notes and practice.

NOTE ON BOARD:

  • Multiples of 4: 4, 8, 12, 16...
  • Multiples of 6: 6, 12, 18...
  • LCM of 4 and 6 = 12
  • Factors of 12: 1, 2, 3, 4, 6, 12
  • Factors of 8: 1, 2, 4, 8
  • HCF of 12 and 8 = 4

EVALUATION (5 questions):

  1. Find LCM of 3 and 5
  2. Find HCF of 10 and 15
  3. List first 5 multiples of 6
  4. What is the HCF of 9 and 12?
  5. Which is higher between HCF and LCM of 4 and 8?

CLASSWORK:

  1. LCM of 2 and 10
  2. HCF of 6 and 9
  3. LCM of 4 and 5
  4. HCF of 8 and 12
  5. List 3 common multiples of 3 and 6

ASSIGNMENT:

  1. Define LCM and HCF.
  2. Find LCM of 7 and 14
  3. Find HCF of 18 and 27
  4. Write 5 multiples of 9
  5. List 4 factors of 20

 

PERIOD 3 & 4: LCM and HCF by Formulae and Inspection

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Reviews multiples and factors. Introduces formula: LCM × HCF = Product of the two numbers.

Pupils answer and ask questions.

Step 2 - Explanation

Explains how to use formula and by listing method.

Pupils solve guided problems.

Step 3 - Demonstration

Solves problems using listing and formula.

Pupils try on board and in groups.

Step 4 - Note Taking

Writes key steps and examples on board.

Pupils copy and practice.

NOTE ON BOARD:

  • LCM × HCF = Product of numbers
  • E.g. 4 and 6 → LCM = 12, HCF = 2 → 12 × 2 = 24
  • 4 × 6 = 24

EVALUATION (5 tasks):

  1. Find LCM of 8 and 12 using formula
  2. Find HCF of 15 and 25
  3. Use inspection to find LCM of 5 and 10
  4. Verify: LCM × HCF = product of 6 and 9
  5. List all factors of 24

CLASSWORK:

  1. Find LCM of 7 and 21
  2. HCF of 14 and 28
  3. LCM × HCF of 10 and 15
  4. HCF of 100 and 150
  5. LCM of 12 and 15

ASSIGNMENT:

  1. Find HCF and LCM of 9 and 18
  2. Use formula to confirm product = LCM × HCF
  3. Write 4 multiples of 8
  4. Write 3 factors of 36
  5. Use inspection to find LCM of 10 and 20

PERIOD 5: Application in Quantitative Reasoning

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Discusses when LCM and HCF are useful in real life (schedules, planning, grouping).

Pupils contribute ideas.

Step 2 - Drill

Gives quantitative reasoning problems using LCM and HCF.

Pupils solve and discuss.

Step 3 - Guided Practice

Solves word problems on the board with class.

Pupils follow and practice.

EVALUATION (5 tasks):

  1. Two buses arrive every 10 and 15 minutes. When will they meet again?
  2. Find HCF of 20 and 30
  3. A boy has 12 oranges and 16 mangoes. Find max number of equal packs.
  4. LCM of 4, 6, and 8
  5. Find difference between HCF and LCM of 3 and 9

CLASSWORK:

  1. HCF of 30 and 45
  2. Word problem involving grouping using HCF
  3. LCM of 5 and 20
  4. Word problem using LCM
  5. Fill in blanks: ___ × ___ = 60 (LCM and HCF of 6 & 10)

ASSIGNMENT:

  1. Create 2 word problems using LCM
  2. Solve and explain them
  3. Use formula to verify answers
  4. Write 3 real-life uses of LCM/HCF

Write a quantitative reasoning question and solve it