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 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 = 2² x 3
16 = 4 X 4 = 2 x 2 x 2 x 2 = 2² x2²
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 =
2x515 =
3x530 =
2x3x5LCM 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 =
1,2,4and 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 =
1,2,4and 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 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
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.