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Subject: Mathematics
Semester: 1
Period: 3
Week: 15
School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 4
Date: Week 15
Lesson Duration: 45 minutes
Week & Period: Week 15, Period 3
Topic: LCM and GCF
Sub-topic: Finding Least Common Multiple and Greatest Common Factor
Learning Objectives
By the end of the lesson, students should be able to:
- Define and find the Least Common Multiple (LCM) of numbers.
- Define and find the Greatest Common Factor (GCF) of numbers.
- Solve word problems involving LCM and GCF.
Previous Knowledge
Students already know factors, multiples, and prime factors.
Instructional Materials
Mathematics textbook for Grade 4, multiplication charts.
Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher asks: “What are the multiples of 6? What are the multiples of 8?” Then asks: “Which multiples appear in both lists?”
B – Building Knowledge (Main Lesson Body)
Time: 25–30 minutes
Definition: The Least Common Multiple (LCM) is the smallest positive number that is a multiple of two or more numbers. It is the first number that appears in the multiples list of each number.
Example:
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
- Multiples of 6: 6, 12, 18, 24, 30, ...
The smallest common multiple is 12, so LCM(4, 6) = 12.
Definition: The Greatest Common Factor (GCF) (also called Greatest Common Divisor) is the largest number that divides two or more numbers exactly without leaving a remainder. It is the biggest factor that both numbers share.
Example:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
The greatest common factor is 6, so GCF(12, 18) = 6.
Methods to find LCM and GCF:
- Listing multiples or factors: Write out multiples (for LCM) or factors (for GCF) of the numbers and identify the smallest common multiple or largest common factor.
- Prime factorization: Break down both numbers into their prime factors.
- For LCM: Take each prime factor the highest number of times it appears in any number.
- For GCF: Take each prime factor the lowest number of times it appears in all numbers.
Example using prime factorization:
Find LCM and GCF of 12 and 18.
- 12 = 2² × 3
- 18 = 2 × 3²
LCM: Take the highest powers → 2² × 3² = 4 × 9 = 36
GCF: Take the lowest powers → 2¹ × 3¹ = 2 × 3 = 6
Word Problem Example:
Two bells ring every 6 minutes and every 8 minutes. After how many minutes will they ring together?
- Find LCM(6, 8):
Multiples of 6: 6, 12, 18, 24, 30...
Multiples of 8: 8, 16, 24, 32...
Smallest common multiple is 24.
So, they ring together every 24 minutes.
More Examples:
- Find LCM of 5 and 10.
Multiples of 5: 5, 10, 15, 20, ...
Multiples of 10: 10, 20, 30, ...
LCM = 10 - Find GCF of 20 and 30.
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
GCF = 10
Learners’ Activities (Expanded):
- Work in groups to solve: LCM(5, 10), LCM(3, 9), GCF(20, 30), GCF(16, 24).
- Use prime factorization to find LCM and GCF of numbers like 18 and 24, 30 and 45.
- Solve word problems involving real-life scenarios such as scheduling (e.g., bus arrivals, bell rings, traffic light cycles).
- Create their own word problems involving LCM and GCF and solve them with peers.
Assessment Checks:
- What is the LCM of 3 and 4? (Answer: 12)
- What is the GCF of 16 and 24? (Answer: 8)
- List the first five multiples of 7 and 9 and identify the LCM.
- Find the GCF of 36 and 48 using prime factorization.
- Explain in your own words why the GCF is useful in dividing items equally.
Notes (Expanded & Detailed):
The LCM helps in finding when repeated events coincide, such as bus schedules or ringing bells. It is essential in solving problems that involve adding or subtracting fractions with unlike denominators.
The GCF is helpful for dividing things into equal groups without leftovers, such as sharing resources evenly, simplifying fractions, or finding common denominators.
Both concepts rely heavily on prime factorization for efficient computation and help students understand the structure and relationships between numbers.
Extended Practice Assignments:
- Find the LCM and GCF of the following pairs: (8, 12), (15, 25), (24, 36), (40, 60).
- Write two word problems involving LCM and solve them.
- Explain why the LCM is always greater than or equal to the greatest number in the set.
- Find the GCF of 54 and 72 using factor trees.
- Using multiples, determine after how many minutes two traffic lights, changing every 15 and 20 minutes respectively, will turn green at the same time.
This detailed explanation, along with activities, examples, and assessments, ensures learners deeply understand LCM and GCF, and can apply them effectively in problem-solving situations.
C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: LCM is the smallest common multiple; GCF is the largest common factor.
Evaluation Method (Expanded):
Exit slip/quiz: Find LCM(6,9) and GCF(18,24).
Teacher will collect slips and provide oral feedback.
Assignment (Expanded):
Solve three word problems: two for LCM, one for GCF.
Follow-up Activity:
Students practice by finding LCM and GCF of numbers around their age.
Differentiation / Inclusive Strategies
Teacher provides multiplication and factor charts for struggling learners.
Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low