### Lesson Plan: Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of Whole Numbers
#### Grade Level: Junior Secondary 1
---
**Subject:** Mathematics
**Topic:** Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of Whole Numbers
**Duration:** 1 hour
**Materials Needed:** Whiteboard, markers, projector (optional), worksheets, calculators
---
#### Objectives:
By the end of the lesson, students will be able to:
1. Understand the concepts of Least Common Multiple (LCM) and Greatest Common Divisor (GCD).
2. Calculate the LCM and GCD of two or more whole numbers using different methods.
3. Apply the concepts of LCM and GCD in solving real-life problems.
---
### Introduction (10 minutes)
1. **Greeting and Attendance:** Greet students and take attendance.
2. **Warm-up Activity:** Begin with a quick review of prime numbers and multiplication tables to refresh students' memory.
3. **Objective Introduction:** Briefly introduce the day's objectives and why understanding LCM and GCD is important in both math and everyday life.
### Direct Instruction (15 minutes)
1. **Definitions:**
- Explain what LCM is: “The smallest number that is a multiple of two or more numbers.”
- Explain what GCD (also known as Greatest Common Factor or GCF) is: “The largest number that divides two or more numbers without leaving a remainder.”
2. **Methods to Find LCM:**
- **Listing Multiples Method:** Show how to list the multiples of given numbers and find the smallest common multiple.
- **Prime Factorization Method:** Explain how to find the LCM using prime factorization of each number and taking the highest powers of all prime factors.
3. **Methods to Find GCD:**
- **Listing Factors:** Show how to list all factors of given numbers and find the greatest common factor.
- **Prime Factorization:** Explain how to use prime factorization to find common prime factors and multiply them to get the GCD.
- **Euclidean Algorithm:** Briefly introduce the Euclidean algorithm for finding the GCD for advanced students.
### Guided Practice (20 minutes)
1. **Examples:**
- Work through several examples on the board with the class, first demonstrating each step then gradually involving students in the process.
- LCM Example: Find the LCM of 12 and 15.
- List multiples: 12: 12, 24, 36, 48, 60... 15: 15, 30, 45, 60...
- LCM: 60
- GCD Example: Find the GCD of 18 and 24.
- Prime Factorization:
- 18: \(2 \times 3^2\)
- 24: \(2^3 \times 3\)
- Common factors: \(2 \times 3 = 6\)
- GCD: 6
2. **Student Practice:**
- Distribute worksheets with problems on LCM and GCD.
- Roam the classroom to assist and provide feedback.
### Independent Practice (10 minutes)
1. **Worksheet Activity:** Allow students to complete a set of exercises on their own. Ensure a mix of problems that require both listing, prime factorization, and the Euclidean algorithm (if applicable).
### Assessment (5 minutes)
1. **Quick Quiz:** Give a brief quiz with a few questions to evaluate student understanding. Examples:
- Find the LCM of 8 and 12.
- Find the GCD of 30 and 45.
2. **Review Answers:** Go over the answers as a class and address any common errors or misconceptions.
### Conclusion (5 minutes)
1. **Recap:** Ask students to summarize what they learned about LCM and GCD.
2. **Real-World Application:** Discuss real-world scenarios where calculating LCM and GCD might be useful, such as finding cycles in repeating events or simplifying fractions.
3. **Homework:** Assign homework that includes a mix of LCM and GCD problems for further practice.
---
### Additional Notes:
- **Differentiation:** Provide additional support for struggling students through one-on-one help or small group instruction.
- **Extension:** Offer challenging problems for advanced students, such as involving more than two numbers or using larger numbers.
- **Follow-Up:** Plan a follow-up lesson to reinforce these concepts and explore their applications in solving word problems.
---
This structured lesson plan aims to provide Junior Secondary 1 students with a comprehensive understanding of LCM and GCD, supporting lifelong mathematical competence.