Finding the LCM of 2 or 3 digits using the Multiple Method and Prime Factors Method Mathematics Primary 6 First Term Lesson Notes Week 5

Subject: Mathematics

Class : Primary 6

Topic: Finding the LCM of 2 or 3 digits using the Multiple Method and Prime Factors Method

Duration: 1 hour

Term: First Term

Week: 5

Previous Lesson: Factors and Multiples

Learning Objectives: By the end of this lesson, students should be able to:

1. Understand the concept of LCM (Least Common Multiple).
2. Find the LCM of two or three-digit numbers using the Multiple Method.
3. Find the LCM of two or three-digit numbers using the Prime Factors Method.

Embedded Core Skills:

• Problem-solving
• Numeracy
• Critical thinking

Learning Materials:

• Chalkboard or whiteboard
• Chalk or markers
• Examples of two or three-digit numbers
• Worksheets for practice
• Prime factorization charts (if available)

Content:

What’s the LCM? The LCM is the smallest number that is a multiple of two or more numbers. It’s like finding the common ground where different numbers meet.

Example 1: Find the LCM of 12 and 18

1. List the Multiples:
   • Multiples of 12: 12, 24, 36, 48, 60, …
   • Multiples of 18: 18, 36, 54, 72, 90, …
2. Identify the Common Multiple:
   • The first common multiple in both lists is 36.

So, the LCM of 12 and 18 is 36.

Example 2: Find the LCM of 3, 4, and 5

1. List the Multiples:
   • Multiples of 3: 3, 6, 9, 12, 15, …
   • Multiples of 4: 4, 8, 12, 16, 20, …
   • Multiples of 5: 5, 10, 15, 20, 25, …
2. Identify the Common Multiple:
   • The first common multiple in all three lists is 12.

So, the LCM of 3, 4, and 5 is 12.

Remember:

• Listing the multiples helps us find the smallest number that all the given numbers can go into.
• The LCM is the smallest common multiple.

Now, you can use this method to find the LCM of any two or three-digit numbers!

Step 1: Find the Prime Factors

• First, we find the prime factors of each number. Prime factors are the smallest prime numbers that can divide a number evenly.

Example 1: Find the LCM of 18 and 24

• Prime factors of 18: 2 × 3 × 3
• Prime factors of 24: 2 × 2 × 2 × 3

Step 2: List All Prime Factors

• Write down all the prime factors from both numbers.

Example 1 (continued):

• List of prime factors: 2, 2, 2, 3, 3

Step 3: Multiply the Prime Factors

• Multiply all the prime factors together.

Example 1 (continued):

• 2 × 2 × 2 × 3 × 3 = 72

So, the LCM of 18 and 24 is 72.

Example 2: Find the LCM of 12, 15, and 20

• Prime factors of 12: 2 × 2 × 3
• Prime factors of 15: 3 × 5
• Prime factors of 20: 2 × 2 × 5
• List of prime factors: 2, 2, 3, 3, 5
• Multiply the prime factors: 2 × 2 × 3 × 3 × 5 = 180

So, the LCM of 12, 15, and 20 is 180.

Remember:

• Prime factors are the smallest prime numbers that can divide a number evenly.
• List all the prime factors from all the numbers.
• Multiply them together to find the LCM.

Now you know how to find the LCM using the prime factors method

Step 1: List the Factors

• First, list all the factors of each number. Factors are the numbers that can divide another number without leaving a remainder.

Example 1: Find the HCF of 12 and 18

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

Step 2: Identify Common Factors

• Identify the common factors that appear in the factor lists of all the given numbers.

Example 1 (continued):

• Common factors: 1, 2, 3, 6

Step 3: Find the Largest Common Factor

• From the common factors, find the largest one. This is the HCF.

Example 1 (continued):

• Largest common factor: 6

So, the HCF of 12 and 18 is 6.

Example 2: Find the HCF of 15, 20, and 25

• Factors of 15: 1, 3, 5, 15
• Factors of 20: 1, 2, 4, 5, 10, 20
• Factors of 25: 1, 5, 25
• Common factors: 1, 5
• Largest common factor: 5

So, the HCF of 15, 20, and 25 is 5.

Remember:

• Factors are numbers that can divide another number without leaving a remainder.
• List all the factors of each number.
• Identify the common factors.
• Find the largest common factor, which is the HCF.

Now you know how to find the HCF using the factor method!

Multiple Method:

1. The LCM is the ___________ multiple of two or more numbers. a) smallest b) biggest c) even d) odd
2. To find the LCM using the multiple method, we list the ___________ of each number. a) words b) meanings c) factors d) colors
3. In the multiple method, we look for the first common ___________ in the lists of multiples. a) odd number b) smallest number c) multiple d) big number
4. What is the LCM of 8 and 12? a) 6 b) 16 c) 24 d) 30
5. To find the LCM of 3, 4, and 6, we list the multiples of each number and look for the first ___________ multiple. a) even b) common c) large d) strange

Prime Factors Method:

6. The prime factors of a number are the ___________ prime numbers that can divide it. a) biggest b) smallest c) largest d) colorful
7. In the prime factors method, we first find the prime factors of ___________ number. a) just one b) all c) no d) odd
8. To find the LCM using prime factors, we list all the ___________ factors from the given numbers. a) small b) prime c) even d) colorful
9. What are the prime factors of 18? a) 2 × 2 × 3 b) 3 × 5 c) 1 × 18 d) 4 × 4
10. In the prime factors method, we ___________ the prime factors to find the LCM. a) add b) multiply c) subtract d) divide

Both Methods:

11. To find the LCM, you can use ___________ or prime factors method. a) only one b) neither c) both d) the biggest
12. The LCM is the ___________ common multiple of the given numbers. a) largest b) smallest c) only d) colorful
13. What is the LCM of 15, 20, and 25? a) 5 b) 10 c) 15 d) 25
14. To find the LCM, you need to find the ___________ number that all given numbers can go into. a) biggest b) smallest c) most colorful d) rarest
15. In the prime factors method, the LCM is found by multiplying the ___________ prime factors. a) smallest b) biggest c) most colorful d) most valuable

Presentation:

Step 1 – Introduction (10 minutes)

• Start by discussing what the LCM (Least Common Multiple) means. Use simple language to explain.
• Introduce the two methods that will be covered in the lesson: the Multiple Method and the Prime Factors Method.

Step 2 – The Multiple Method (20 minutes)

• Explain the Multiple Method:
  • List multiples of two or three-digit numbers.
  • Identify the first common multiple.
  • This is the LCM.
• Provide examples and practice questions on the board.
• Encourage students to solve problems on their own or in pairs.

Step 3 – The Prime Factors Method (20 minutes)

• Explain the Prime Factors Method:
  • Find the prime factors of each number.
  • List all prime factors.
  • Multiply prime factors to find the LCM.
• Provide examples and practice questions on the board.
• Encourage students to solve problems using this method.

Teacher’s Activities:

• Explain the concepts using simple language.
• Provide clear examples.
• Monitor students’ progress and offer assistance as needed.
• Encourage class participation and questions.

Learners’ Activities:

• Listen attentively and take notes.
• Solve practice problems individually or in pairs.
• Ask questions for clarification.
• Participate actively in class discussions.

Assessment:

• Assess students’ ability to find the LCM using both methods.
• Evaluate their problem-solving skills.

Fill-in-the-Gap Evaluation Questions:

1. The LCM stands for __________ Common Multiple. a) Least b) Largest c) Last d) Little
2. To find the LCM using the Multiple Method, we list the __________ of the given numbers. a) factors b) prime factors c) multiples d) fractions
3. In the Prime Factors Method, we find the __________ of each number. a) prime factors b) least common multiple c) greatest common factor d) factors
4. The first common multiple in the Multiple Method is the __________. a) largest b) smallest c) oddest d) most colorful
5. What is the LCM of 9 and 12 using the Multiple Method? a) 3 b) 18 c) 27 d) 36
6. The Prime Factors Method involves finding the __________ of each number. a) multiples b) factors c) common factors d) prime factors
7. To find the LCM using the Prime Factors Method, we multiply the __________ prime factors. a) smallest b) largest c) oddest d) even
8. What are the prime factors of 24? a) 2 × 2 × 2 × 3 b) 1 × 24 c) 5 × 5 d) 10 × 10
9. Find the LCM of 6 and 8 using the Prime Factors Method. a) 12 b) 24 c) 48 d) 96
10. The LCM is the __________ common multiple of given numbers. a) largest b) smallest c) oddest d) most colorful

Conclusion on the Topic: In this lesson, we learned how to find the LCM (Least Common Multiple) of two or three-digit numbers using two different methods: the Multiple Method and the Prime Factors Method. The LCM helps us find the smallest common multiple, and these methods make it easier to find it. Keep practicing, and you’ll become a master at finding LCM!