# LCM and HCF not more than 2 Digit Whole Numbers Primary 6 (Basic 6) – Mathematics

### MATHEMATICS

FIRST TERM

WEEK 4

PRIMARY 6

THEME – NUMBER AND NUMERATION

PREVIOUS LESSON –

### LEARNING AREA

1. Introductory Activities

2. LCM and HCF

3. Lesson Evaluation and Weekly Assessment (Test)

### PERFORMANCE OBJECTIVES

By the end of the lesson, most pupils should have attained the following objectives –

1. find the LCM and HCF of 3 digit whole numbers.

2. solve quantitative aptitude problem on LCM and HC F.

### ENTRY BEHAVIOUR

The pupils can perform basic mathematics operations like multiplication and division.

### INSTRUCTIONAL MATERIALS

The teacher will teach the lesson with the aid of multiplication table.

### METHOD OF TEACHING

Choose a suitable and appropriate methods for the lessons.

Note – Irrespective of choosing methods of teaching, always introduce an activities that will arouse pupil’s interest or lead them to the lessons.

### REFERENCE MATERIALS

1. Scheme of Work

2. 9 – Years Basic Education Curriculum

3. Course Book

4. All Relevant Material

5. Online Information

### LESSON 1 – INTRODUCTION

ACTIVITY 1 – MULTIPLE OF A WHOLE NUMBER

2 – 2 4 6 8 10 12 14 16 18 20….

3 – 3 6 9 12 15 18 21 24 27 30….

4 – 4 8 16 20 24 28 32 36 40….

5 – 5 10 15 20 25 30 35 40 55 50….

6 – 6 12 18 24 30 36 42 48 54 60….

7 – 7 14 21 28 35 42 49 56 63 70….

8 – 8 16 24 32 40 48 56 64 72 80….

9 – 9 18 27 36 45 54 63 72 81 90….

10 – 10 20 30 40 50 60 70 80 90 100….

ACTIVITY 2 – COMMON MULTIPLE

2 – 2 4 6 8 10 12 14 16 18 20

3 – 3 6 9 12 15 18 21 24 27 30

Common Multiple of 2 and 3 is 12.

4 – 4 8 16 20 24 28 32 36 40

5 – 5 10 15 20 25 30 35 40 55 50

Common Multiples of 4 and 5 are 20 and 40

4 – 4 8 16 20 24 28 32 36 40

8 – 8 16 24 32 40 48 56 64 72 80

Common Multiples of 4 and 8 are 8 6 24 32 and 40

Common Multiples is a multiple that is shared between two or more numbers.

ACTIVITY 3 – LCM

LCM stands for Least Common Multiple.

The least common multiple of a number is the smallest number that is the product of two or more numbers.

For examples,

1. LCM of 2 and 3

2 – 2 4 6 8 10 12 14 16 18 20

3 – 3 6 9 12 15 18 21 24 27 30

Common Multiple of 2 and 3 is 12.

The least common multiple is 12.

2. LCM of 4 and 5

4 – 4 8 16 20 24 28 32 36 40

5 – 5 10 15 20 25 30 35 40 55 50

Common Multiples of 4 and 5 are 20 and 40

Since, 20 is less than 40 amd 40 is greater than 20.

Therefore, the least common multiple is 20.

3. LCM of 4 and 8

4 – 4 8 16 20 24 28 32 36 40

8 – 8 16 24 32 40 48 56 64 72 80

Common Multiples of 4 and 8 are 8 6 24 32 and 40

The least common multiple is 8.

LCM OF 2 DIGIT WHOLE NUMBERS

There are 3 methods to find the least common multiple of two numbers.

1. Listing method

2. Prime factor method

3. Division method

Note – The listen method is illustrated in activity 3.

ACTIVITY 4

1. LCM of 12 and 16

12 = 4 X 3 = 2 x 2 x 3 = x 3

16 = 4 X 4 = 2 x 2 x 2 x 2 = x

Common Multiple is 2² x 2² x 3 = 4 x 4 x 3

LCM of 12 and 16 is 2² x 2² x 3 = 4 x 4 x 3 = 48.

Alternative method,

2 | 12, 16

2 |   6,    8

2 |   3,    4

2 |   3,    2

3 |   3,    1

1,    1

LCM of 12 and 16 is 2 x 2 x 2 x 2 x 4 = 48

2. LCM of 10, 15 and 30

2 | 10, 15, 30

3 |   5, 15, 15

5 |   5,    5,  5

|   1,   1,   1

LCM of 10, 15 and 30 is 2 x 3 x 5 = 30

Alternative method,

10 = 2 x 5

15 = 3 x 5

30 = 2 x 3 x 5

LCM of 10, 15 and 30 is 2 x 3 x 5 = 30

OR,

10 = 10, 20, 30, 40, 50, 60, 70,….

15 = 15, 30, 45, 60, 75, 90, 105,….

30 = 30, 60, 90, 120, 150, 180, 210,….

Common Multiples are 30 and 60.

The least common multiple of 10, 15 and 30 is 30.

LESSON EVALUATION

Find the LCM of –

1. 6 and 9

2. 6, 8 and 9

3. 16 and 32

4. 12, 18 and 36

Note – You can use any method you find easy.

### LESSON 2 – CONTINUATION

LCM of 36, 54 and 84

2 | 36, 54, 84

2 | 18, 27, 42

2 |   9, 27, 21

3 |    3,    9,  7

3 |    1,    3,  7

7 |    1,    1,  7

1,    1,  1

LCM of 36, 54 and 84 is 2 x 2 x 2 x 3 x 3 x 7 = 504

Take one or more challenge examples.

LESSON EVALUATION

Find the LCM of

1. 54 and 48

2. 12, 54 and 46

### LESSON 3 – HCF

ACTIVITY 1 – FACTORS OF WHOLE NUMBERS

1 = 1

2 = 1 and 2

3 = 1 and 3

4 = 1, 2 and 4

5 = 1 and 5

6 = 1, 2, 3 and 6

7 = 1 and 7

8 = 1, 2, 4 and 8

9 = 1, 3 and 9

10 = 1, 2, 5 and 10

A factor is a number that divides the given number without any remainder.

ACTIVITY 2 – COMMON FACTORS

6 = 1, 2, 3 and 6

8 = 1, 2, 4 and 8

Common factors of 6 and 8 are 1 and 2.

8 = 1, 2, 4 and 8

12 = 1, 2, 3, 4, 6 and 12

Common factors are 1, 2 and 4

16 = 1, 2, 4, 8 and 16

24 = 1, 2, 3, 4, 6, 8, 12 and 24

Common factors are 1, 2, 4, 6 and 8.

ACTIVITY 3 – HCF

HCF stands for Highest Common Factors.

The Highest Common Factor of who numbers is the greatest number which divides exactly the given numbers.

There are three methods of finding HCF of whole numbers,

1. Factor Method

2. Prime Factorization Method

3. Division Method

Examples,

HCF of 6 and 6

6 = 1, 2, 3 and 6

8 = 1, 2, 4 and 8

Common factors of 6 and 8 are 1 and 2.

Since 2 is greater than 1,

Therefore,

The HCF is 2.

HCF of 8 and 12

8 = 1, 2, 4 and 8

12 = 1, 2, 3, 4, 6 and 12

Common factors are 1, 2 and 4.

The HCF of 8 and 12 is 4.

16 = 1, 2, 4, 8 and 16

24 = 1, 2, 3, 4, 6, 8, 12 and 24

Common factors are 1, 2, 4, 6 and 8.

The HCF of 16 and 24 is 8.

ACTIVITY 4 – ALTERNATIVE METHOD

1. HCF of 10, 15 and 30

5 | 10, 15, 30

2,   3,   6

HCF of 10, 15 and 30 is 5.

2. HCF of 36, 56 and 84

2 | 36, 56, 84

2 | 18, 28, 42

9, 14, 21

HCF of 36, 54 and 84 is 2 x 2 = 4.

LESSON EVALUATION

Find the HCF of

1. 15, 20 and 25

2. 16, 54 and 72

3. 54 and 72

4. 28 and 56

### PRESENTATION

To deliver the lesson, the teacher adopts the following steps – he/she,

1. Revises the previous lesson based on the pupil’s related knowledge or experience.

Pupil’s Activities – Participate actively in the lesson review.

2. Displays multiplication chart.

3. Uses the chart to guide the pupils to find multiple, common multiple and LCM of two or more whole numbers.

Pupil’s Activities – Follow the teacher’s guidelines to find the LCM of two or more whole numbers.

4. Uses the chart to guide the pupils to find factors, common factors and HCF of two or more whole numbers.

Pupil’s Activities – Follow the teacher’s guidelines to find the factors, common factors and HCF of two or more whole numbers.

### CONCLUSION

To conclude the lesson for the week, the teacher revises the entire lesson and links it to the following week’s lesson.

### LESSON EVALUATION

As state in the lesson evaluation.