L.C.M and H.C.F Mastering L.C.M and H.C.F: Techniques and Applications Mathematics Primary 6 First Term Lesson Notes Week 5

Lesson Plan for Week 5

Subject: Mathematics
Class: Primary 6
Term: First Term
Week: 5
Age: 11 years
Topic: L.C.M (Lowest Common Multiple) and H.C.F (Highest Common Factor)
Sub-Topic: L.C.M and H.C.F of 2 or 3 Digits, Real-Life Problems, and Quantitative Reasoning
Duration: 60 minutes

Behavioral Objectives

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

1. Find the L.C.M of 2 or 3-digit numbers using both the multiple method and prime factors method.
2. Determine the H.C.F of any given 2 or 3-digit numbers using the factor method.
3. Interpret and solve real-life problems related to L.C.M and H.C.F.
4. Solve quantitative reasoning questions related to L.C.M and H.C.F.

Keywords

• L.C.M (Lowest Common Multiple)
• H.C.F (Highest Common Factor)
• Multiples
• Prime Factors
• Factors
• Real-life Problems
• Quantitative Reasoning

Set Induction

Introduce the topic by discussing everyday scenarios where finding common multiples or factors is useful, such as scheduling events or dividing resources evenly.

Entry Behavior

Pupils should be familiar with basic multiplication and division concepts, as well as finding factors and multiples of smaller numbers.

Learning Resources and Materials

• Charts for L.C.M and H.C.F methods
• Worksheets with practice problems
• Flashcards with real-life scenarios

Building Background/Connection to Prior Knowledge

Link the lesson to previous topics on multiplication and division, explaining how L.C.M and H.C.F are related to these operations and are used to solve more complex problems.

Embedded Core Skills

• Analytical Thinking
• Problem-Solving
• Mathematical Reasoning

Learning Materials

• Lagos State Scheme of Work
• L.C.M and H.C.F charts
• Example problems on the board
• Real-life problem scenarios

Reference Books

• Lagos State Scheme of Work
• New General Mathematics for Primary Schools

Instructional Materials

• Charts and flashcards
• Chalkboard/Whiteboard
• Markers/Chalk

Content

1. Finding the L.C.M of 2 or 3 Digits
   • Multiple Method:
     • List the multiples of each number until a common multiple is found.
     • Example: Find L.C.M of 12 and 15.
       • Multiples of 12: 12, 24, 36, 48, 60…
       • Multiples of 15: 15, 30, 45, 60…
       • L.C.M is 60.
   • Prime Factors Method:
     • Find the prime factors of each number and multiply the highest powers of all prime factors.
     • Example: Find L.C.M of 12 and 15.
       • Prime factors of 12: 2² × 3
       • Prime factors of 15: 3 × 5
       • L.C.M is 2² × 3 × 5 = 60.
2. Finding the H.C.F of 2 or 3 Digits
   • Factor Method:
     • List the factors of each number and find the highest common factor.
     • Example: Find H.C.F of 18 and 24.
       • Factors of 18: 1, 2, 3, 6, 9, 18
       • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
       • H.C.F is 6.
3. Real-Life Problems Involving L.C.M and H.C.F
   • Example: If two events repeat every 6 days and 8 days, when will they both occur on the same day again?
     • Use L.C.M to find that they will both occur on the same day every 24 days.
4. Quantitative Reasoning Problems Related to L.C.M and H.C.F
   • Practice problems that involve using L.C.M and H.C.F to solve more complex questions.

Questions

1. The L.C.M of 8 and 12 is _______.
   a) 24
   b) 12
   c) 48
   d) 20
2. What is the H.C.F of 36 and 48?
   a) 12
   b) 18
   c) 24
   d) 6
3. The L.C.M of 15 and 20 is _______.
   a) 60
   b) 30
   c) 45
   d) 40
4. What is the H.C.F of 28 and 35?
   a) 7
   b) 14
   c) 5
   d) 10
5. The L.C.M of 5 and 7 is _______.
   a) 35
   b) 70
   c) 10
   d) 12
6. What is the H.C.F of 50 and 75?
   a) 25
   b) 50
   c) 15
   d) 10
7. The L.C.M of 9 and 12 is _______.
   a) 36
   b) 18
   c) 24
   d) 12
8. What is the H.C.F of 60 and 90?
   a) 30
   b) 60
   c) 15
   d) 45
9. The L.C.M of 14 and 21 is _______.
   a) 42
   b) 28
   c) 56
   d) 14
10. What is the H.C.F of 84 and 108?
    a) 12
    b) 24
    c) 36
    d) 18
11. The L.C.M of 16 and 24 is _______.
    a) 48
    b) 32
    c) 64
    d) 24
12. What is the H.C.F of 45 and 60?
    a) 15
    b) 30
    c) 45
    d) 5
13. The L.C.M of 18 and 27 is _______.
    a) 54
    b) 36
    c) 27
    d) 81
14. What is the H.C.F of 100 and 150?
    a) 50
    b) 100
    c) 25
    d) 75
15. The L.C.M of 30 and 45 is _______.
    a) 135
    b) 90
    c) 60
    d) 45

Class Activity Discussion

1. Q: What is the L.C.M?
   A: The Lowest Common Multiple is the smallest number that is a multiple of two or more numbers.
2. Q: How do you find the L.C.M using the multiple method?
   A: List the multiples of each number until you find the smallest common multiple.
3. Q: What is the H.C.F?
   A: The Highest Common Factor is the largest number that divides two or more numbers without leaving a remainder.
4. Q: How do you find the H.C.F using the factor method?
   A: List all factors of each number and choose the largest common factor.
5. Q: What is the difference between L.C.M and H.C.F?
   A: L.C.M is the smallest common multiple of numbers, while H.C.F is the largest common factor.
6. Q: How do you find the L.C.M using prime factors?
   A: Break each number into its prime factors, then multiply the highest powers of all prime factors.
7. Q: What is the L.C.M of 10 and 15?
   A: 30
8. Q: What is the H.C.F of 20 and 25?
   A: 5
9. Q: How can you solve real-life problems using L.C.M and H.C.F?
   A: Apply L.C.M to find common schedules or event timings and H.C.F to distribute items evenly.
10. Q: How do you handle large numbers when finding L.C.M and H.C.F?
    A: Use prime factorization or multiples to simplify calculations.
11. Q: What is the L.C.M of 21 and 28?
    A: 84
12. Q: How do you find the H.C.F of three numbers?
    A: Find the H.C.F of the first two numbers, then find the H.C.F of the result with the third number.
13. Q: What is the L.C.M of 8, 12, and 18?
    A: 72
14. Q: How do you apply H.C.F in real-life scenarios?
    A: Use H.C.F to divide items into equal parts or to find the greatest size of groups.
15. Q: What is the L.C.M of 6, 9, and 15?
    A: 90

10 Evaluation Questions

1. Find the L.C.M of 12 and 18.
2. Determine the H.C.F of 48 and 60.
3. Calculate the L.C.M of 14 and 28.
4. What is the H.C.F of 81 and 108?
5. Solve: Find the L.C.M of 24 and 36.
6. Determine the H.C.F of 42 and 56.
7. Find the L.C.M of 10, 15, and 20.
8. What is the H.C.F of 30 and 75?
9. Calculate the L.C.M of 8 and 14.
10. Determine the H.C.F of 36, 54, and 72.

Conclusion

• Recap the methods for finding L.C.M and H.C.F.
• Ensure pupils can solve real-life problems using these concepts.
• Assign additional problems for practice to reinforce learning.