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# Whole Numbers – LCM and HCM

MATHEMATICS

FIRST TERM

FOURTH WEEK

BASIC 6

TOPIC: LCM and HCF

LCM means Least Common Multiple. HCF means Highest Common Factor. LCD means Least Common Denominator.

PERFORMANCE OBJECTIVES

By the end of the lesson, the pupils should have attained the following objectives (cognitive, affective and psychomotor) and be able to:

1. find the LCM and HCF of 2-digit whole numbers;
2. solve quantitative aptitude problem on LCM and HCF.

ENTRY BEHAVIOR

Multiplication table up to 12 x 12.

INSTRUCTIONAL MATERIALS

The teacher will teach the lesson with the aid of Charts of factors of numbers.

METHOD OF TEACHING

1. Inquiry
2. Discovery

REFERENCE MATERIALS

1. Scheme of Work
2. 9 – Years Basic Education Curriculum
3. New Method Mathematics Book 6
4. All Relevant Materials
5. MathIsFun

CONTENT OF THE LESSON

REVISION OF LCM OF 1-DIGIT NUMBERS

Factors are numbers we can multiply together to get another number. Every number (except 1) has two or more factors.

NUMBER WITH ONLY ONE FACTOR

1 is the only number that has only one factor.

NUMBERS WITH ONLY TWO FACTORS

• 2 = 1 x 2, 2 has 1 and 2 as a factor

• 3 = 1 x 3, 3 has 1 and 3 as a factor

• 5 = 1 x 5, 5 has 1 and 5 as a factor

• 7 = 1 x 7, 7 has 1 and 7 as a factor

Note: A prime number is a whole number greater than 1 whose has only two factors. That’s, 1 and itself.

NUMBERS WITH MORE THAN TWO FACTORS

• 4 = 1 x 4, 2 x 2. 4 has 1, 2 and 4 as a factor

• 6 = 1 x 6, 2 x 3. 6 has 1, 2, 3 and 6 as a factor

• 8 = 1 x 8, 2 x 4. 8 has 1, 2, 4, and 8 as a factor

• 9 = 1 x 9, 3 x 3. 9 has 1, 3 and 9 as a factor

• 10 = 1 x 10, 2 x 5.10 has 1, 2 and 10 as a factor

• 36 = 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6. 36 has 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Note: 1 is a factor of all numbers.

• Find the factor of:

1. 12
2. 15
3. 18.

MULTIPLE

The multiples of a whole number are the result we get after multiplying the number by another number, e.g. Multiple of 2 are 2, 4, 6, 8, 10, 12, and so on. Check out the multiplication table.

COMMON MULTIPLE

These are the common result between two or more numbers

• Find the multiple of:
1. 12 ___ ___ ___ ___ ___ 72
2. 15 ___ ___ ___ ___ ___ 90
3. 18 ___ ___ ___ ___ ___ 108.

LEAST COMMON MULTIPLE (LCM)

METHODS

The Multiple Method

The multiple of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22,  ………

The multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, ………

The multiple of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, ………

• The common multiples between 2 and 3 are 6, 12, 18, ………

Therefore,

The least is 6.

• The common multiples between 2 and 4 are 8, 12, 16, ………

Therefore,

The least is 8.

• The common multiples between 3 and 4 are 12, 24, ………

Therefore,

The least is 12.

• The common multiples between 2,  3 and 4 are 12, 24, ………

Therefore,

The least is 12.

The Prime Factor

• Find the LCM of 10 and 12

10 = 2 x 5

12 = 2 x 6 = 2 x 2 x 3

Therefore,

The LCM is 2 x 2 x 3 x 5 = 60

• Find the LCM of 20, 30 and 40

20 = 2 x 10 = 2 x 2 x 5

30 = 2 x 15 = 2 x 3 x 5

40 = 2 x 20 = 2 x 2 x 10 = 2 x 2 x 2 x 5

Therefore,

The LCM of 20, 30 and 40 is 2 x 2 x 2 x 3 x 5 = 120.

• Find the LCM of:

1. 14, 24, 21
2. 8, 16, 24
3. 15, 20, 10.

LEAST (OR LOWEST) COMMON DENOMINATOR (LCD)

REVISION OF HCF OF 1-DIGIT NUMBERS

• Find the HCF of 6 and 9

4 = 1 x 4, 2 x 2. The factors of 4 are 1, 2 and 4

8 = 1x 8, 2 x 4. The factors of 8 are 12, 4 and 8

Common factors of 4 and 8 are 1, 2 and 4

Therefore,

The HCF of 4 and 8 is 4.

HIGHEST COMMON FACTOR (HCF)

METHODS

The Factor Method

• Find the HCF of 12 and 18

12 = 1 x 12, 2 x 6, 3 x 4. The factors of 12 are 1, 2, 3, 4 and 6

18 = 1 x 18, 2 x 9, 3 x 6. The factors of 18 are 1, 23, 6, 9 and 18

Common Factors are 1, 2, 3 and 6

Therefore,

The HCF of 12 and 18 is 6.

• Find the factors of 16, 30 and 24

16 = 1 x 16, 2 x 8, 4 x 4. The factors of 16 are 1, 2, 4, 8 and 16

30 = 1 x 30, 2 x 15, 3 x 10, 5 x 6. The factors of 30 are 1, 2, 3, 5, 6, 10 and 15

24 = 1 x 24, 2 x 12, 3 x 8, 4 x 6. The factors of 24 are 1, 2, 3, 4, 6 and 8

Common Factors are 1 and 2

Therefore,

The HCF is 2.

• Find the HCF of:

1. 14, 24, 21
2. 8, 16, 24
3. 15, 20, 10.

PRESENTATION

To deliver the lesson, the teacher adopts the following steps:

1. To introduce the lesson, the teacher revises the previous lesson. Based on this, he/she asks the pupils some questions;
2. Guides pupils to revise previous work on LCM of 1-digit numbers;
3. Pupil’s Activities – Revise the previous work on LCM of 1-digit numbers.
4. Guides pupils to write out multiples of numbers say 10 and 1;
5. Guides pupils to find LCM by using factor method and prime factor;
6. Guides pupils to list the common multiples and choose the least common multiple (LCM);
7. Pupil’s Activities – Find the LCM by factor method and compare the two methods of finding LCM.
8. Guides pupils to revise previous work on HCF of 1-digit numbers;
9. Pupil’s Activities – Revise the previous work on HCF of 1-digit number
10. Guides pupils to list the factors of 2-digit numbers;
11. Guides pupils to list the common factors and choose the Highest Common Factor (HCF);
12. Guides pupils to find HCF by using factor method;
13. Pupil’s Activities – Find the HCF by using factor method.
14. Guides pupils to solve quantitative aptitude problem on LCM and HCF;
15. Pupil’s Activities – Solve quantitative aptitude problem on LCM and HCF.

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

Pupils to:

1. find the multiples of given 2-digit numbers;
2. find the LCM of given 2-digit number by factor method and multiple method;
3. find the factors of given whole numbers;
4. find the HCF of given whole numbers;
5. solve some quantitative aptitude problems involving HCF;
6. solve quantitative aptitude problem on LCM and HCF.