HCF & LCM Mathematics Strand : NUMBERS

FOCUS QUESTION

How do I write numbers in the different number system?

SPECIFIC OBJS

1. Read, write and use numbers, using the principle of place value, in the Hindu-Arabic system of numeration.

2. Identify common factors,  HCF  and LCM.

CONTENT SUMMARY

The full forms of H.C.F. and L.C.M. are, Highest Common factor and Least Common Multiple, respectively. The H.C.F. defines the greatest factor present in between given two or more numbers, whereas L.C.M. defines the least number which is exactly divisible by two or more numbers.

ENGAGE

Review what is meant by factors of a number and supply examples.

Is there a difference between factors and multiples?

What are multiples?

Supply some examples.

EXPLORE

Examine the worded problem below, and then try to decipher what is required of you.

There are two Grade 6 classes at Paula’s school. There are eighteen students in one class and twenty-four in the other. Each class has to divide into equal-sized groups to make teams for Sports Day.

(a)    What is the largest number of students that each group will have?

(b)   How many groups will there be in each class?

Think about  the information that you have to work with, and then try to figure out  how you can arrive at the answer. Take turns in discussing how you arrived your answers.

Now examine this video clips which will help you to solve word problems on HCF .

Here are some words to help you determine if you need to find HCF or LCM

 Other Key words .

EXPLAIN

Now can you differentiate between LCM and HCF?

EXTEND/ELABORATE

Try to formulate at least 2 problems related to HCF and  LCM. You may do one of each.

Share your problems with the class.

You can follow the links below to learn more about the topic and to solve other problems relating to the topic.

LCM/HCF

LCM/HCF Samples

LCM and HCF problems

Relationship of LCM & HCF

LCM and HCFhttps://www.youtube.com/watch?v=Ldx1BBmTsF0

EVALUATION

1. Find the greatest number that can divide 204 and 64 without leaving a remainder.

2.  What is the maximum length of equal pieces that can be cut from two lengths of wire of 74 cm and        92 cm with a piece of 2cm remaining of each?

3. Tamara is arranging black marbles in groups of 15 and purple marbles in groups of 25. If she has the same number of black and purple marbles, what is the smallest number of marbles of each colour that she could make?

4. Riya eats at a restaurant every 5th day and  Jordana  eats at a restaurant every 7th day. If they both eat at the restaurant today, how many days until they will eat at the restaurant on the same day?

5.Henry takes 18 Minutes to go completely around a playfield. Sam takes 12 minutes. If both of them start at the same point, how many minutes before will they meet again at the same point?

Mrs. Brown is making party bags. She wants to make  all bags exactly the alike. What is the greatest number of bags she can make?

6, Two students are stacking up blocks. Greg blocks are 4 cm high. Daniel's blocks are 9 cm. How tall will there stack be when they are the same height for the 2nd time?

7. Jack and Jill love when the school's cafeteria serves chicken nuggets and French fries on the same day. Chicken nuggets are served every 5 days and French fries are served every 3 days. If both chicken nuggets and fries are served today, when will they be served together again?

8. Peter is planning his birthday party. His mom said she would make 18 personal pizzas and 27 cupcakes for the party. 

 (a) How many total people can peter have at his party so that the pizzas and cupcakes are shared equally among his friends?

 (b) How many pizzas and cupcakes will each person receive?

Follow up Practice Exercises

Activity 1

Activity 2

Activity 3

Activity 4

Activity 5

Activity 6

Activity 7

Activity 8

📘 5E Model Lesson Plan

Grade Level: 6

Subject: Mathematics
Time: 1 hour
Theme: Common Factors, LCM and HCF
Focus Question: How do I write numbers in the different number systems?

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🔍 ENGAGE (5–7 minutes)

Activity: “Guess the Number System”

• Show students the same number (e.g., 25) written in different number systems (Roman, Binary, Hindu-Arabic).

• Ask:

  • “What do you notice about these numbers?”

  • “Which one do we use every day?”

• Explain that today’s lesson focuses on Hindu-Arabic numeration, which we use to work with numbers including finding common factors, HCF, and LCM.

STEM Connection: Discuss how computers use binary (0s and 1s), but we use Hindu-Arabic numerals to communicate everyday values like time, money, and measurements.

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🧠 EXPLORE (15 minutes)

Activity: Number Grid and Factor Trees (Paired Work)

• Give students a set of numbers (e.g., 12, 16, 18, 24).

• In pairs, students:

  • Use place value to read and write each number correctly in Hindu-Arabic form.

  • Create factor trees to find all factors of the numbers.

  • Circle common factors between number pairs.

  • Identify the HCF and LCM.

Differentiation:

• Tier 1 (Emerging): Use base-10 blocks or grid paper to model numbers and factors.

• Tier 2 (On-level): Use multiplication tables to find factors quickly.

• Tier 3 (Advanced): Challenge to find HCF/LCM of 3 numbers or use prime factorization method.

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📘 EXPLAIN (10–12 minutes)

Mini-Lesson/Discussion

• Guide students through definitions:

  • Place Value: Each digit’s value based on its position in the Hindu-Arabic system.

  • Factor: A number that divides evenly into another.

  • Common Factors: Shared factors between two or more numbers.

  • HCF: The greatest of the common factors.

  • LCM: The smallest number divisible by two or more numbers.

Visual Support: Use a digital whiteboard (or chart paper) to model with color-coded examples.

STEM Link: Highlight real-life STEM examples like:

• LCM: Finding the earliest time two machines with different cycles will operate together.

• HCF: Sharing items equally among groups (e.g., engineers dividing parts equally).

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🧪 ELABORATE (15 minutes)

Activity: “STEM in Action – Robot Reboot!”

• Scenario: Two robots beep at different intervals (Robot A every 6 mins, Robot B every 8 mins).

  • Ask: When will they beep together again? (Find the LCM).

  • Then: How often can both robots recharge using the same battery cycles (Find HCF of given numbers).

Tools: Use math manipulatives or a digital simulation tool (like an LCM calculator or interactive website).

Differentiation:

• Tier 1: Use a number line to skip count.

• Tier 2: Use multiplication chart.

• Tier 3: Use prime factorization for LCM and HCF.

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✅ EVALUATE (8–10 minutes)

Three-Tier Evaluation

Tier	Task	Evaluation Criteria
Level 1 (Emerging)	Identify and write numbers in the Hindu-Arabic system (e.g., write 346 and say value of each digit).	Correct place value identification.
Level 2 (On-level)	Find the common factors and HCF of 12 and 18 using factor lists.	Correct listing of all factors and accurate HCF.
Level 3 (Advanced)	Find the LCM of 8, 12, and 16 using prime factorization.	Logical steps, correct prime factor trees, and correct LCM.

Exit Ticket:

• One example of a real-life situation where you might use HCF.

• One example of a real-life situation where you might use LCM.

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🧩 Assessment Tools

• Observation checklist during Explore and Elaborate

• Student notebooks

• Exit Tickets

• Peer assessment during pair tasks

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📚 Resources/Materials

• Factor trees template

• Base-10 blocks or grid paper

• Multiplication charts

• Digital timer or simulation (STEM connection)

• Chart paper/whiteboard

• Printed evaluation worksheets (3-tiered)