# Whole Numbers – LCM and HCM

Last Updated on September 13, 2018 by Alabi M. S.

**MATHEMATICS **

**FIRST TERM **

**FOURTH WEEK **

**BASIC 6**

**TOPIC:** LCM and HCF

**LCM **means Least Common Multiple. **H****CF** means Highest Common Factor. **L****CD** 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:

- find the LCM and HCF of 2-digit whole numbers;
- 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 **

- Inquiry
- Discovery
- Questions and answers

**REFERENCE MATERIALS**

- Scheme of Work
- 9 – Years Basic Education Curriculum
- New Method Mathematics Book 6
- All Relevant Materials
- 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:

- 12
- 15
- 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:

- 12 ___ ___ ___ ___ ___ 72
- 15 ___ ___ ___ ___ ___ 90
- 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:

- 14, 24, 21
- 8, 16, 24
- 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** 1**, **2**, **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**, **2**, **3**, **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:

- 14, 24, 21
- 8, 16, 24
- 15, 20, 10.

**PRESENTATION**

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

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

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