# 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 –

**TOPIC – LCM AND HCF OF 3 DIGITS NUMBERS **

**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

CONTENT OF THE LESSON

**LESSON 1 – INTRODUCTION **

ACTIVITY 1 – MULTIPLE OF A WHOLE NUMBER2 – 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

1214 16 18 203 – 3 6 9

1215 18 21 24 27 30

Common Multiple of 2 and 3 is 12.

4 – 4 8 16

2024 28 32 36405 – 5 10 15

2025 30 354055 50

**Common Multiples of 4 and 5 are 20 and 40**

4 – 4

8162024283236408 –

81624324048 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 – LCMLCM 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

1214 16 18 203 – 3 6 9

1215 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

2024 28 32 36405 – 5 10 15

2025 30 354055 50Common 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

8162024283236408 –

81624324048 56 64 72 80Common Multiples of 4 and 8 are 8 6 24 32 and 40

The least common multiple is 8.

LCM OF 2 DIGIT WHOLE NUMBERSThere 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 41. LCM of 12 and 16

12 = 4 X 3 =

2x2x3=2²x316 = 4 X 4 =

2x2x2x2=2²x2²

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 EVALUATIONFind 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 EVALUATIONFind the LCM of

1. 54 and 48

2. 12, 54 and 46

**LESSON 3 – HCF **

ACTIVITY 1 – FACTORS OF WHOLE NUMBERS1 = 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 FACTORS6 = 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 812 =

~~1~~,~~2~~, 3,~~4~~, 6 and 12Common 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 812 =

~~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 METHOD1. 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

**LESSON 4/5 – REVISION AND WEEKLY ASSESSMENT **

**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.

### NEXT LESSON

**LESSON EVALUATION **

As state in the lesson evaluation.