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TOPIC : NUMBER PATTERNS AND SEQUENCES Sub Topic : 2.7 Common Multiples and Lowest Common Multiple (LCM) Learning Outcomes : i. Find the common multiples of two or three whole numbers. ii. Determine whether a number is the common multiple of two or three given numbers. iii. Determine the LCM of two or three given numbers.

Saturday, June 22, 2013


1 2 4 8

16

Saturday, June 22, 2013


Find the first three common multiples of 2 and 3 Solution Multiples 2 : 2 .

Multiples 3 :

3

4 6

6 6

8 9

10 12 14 16 18 20

12

18 15 18

The first three common multiples of 2 and 3 are 6, 12 and 18 Saturday, June 22, 2013


Lowest Common Multiple (LCM) 1. The lowest common multiple (LCM) of two or three given numbers is the smallest common multiple of the given numbers. 2. The lowest common multiple (LCM) can be found by two methods: (i) Listing down the multiples (ii) Using algorithm

Saturday, June 22, 2013


Example : Find the lowest common multiple 6, 8 and 12. Method (i) Method (ii)

Saturday, June 22, 2013


Listing down the multiples

.

Multiples of 6 :

6

12

18 24 30 36 42 48

Multiples of 8 :

8

16

24 32 40 48

Multiples of 12 :

12

24

36

48

The common multiples of 6, 8 and 12 are 24, 48 Therefore the lowest common multiple (LCM) of 6, 8 and 12 is 24. Saturday, June 22, 2013


Using algorithm 2 6, 8, 12 2 3, 4, 6 2 3, 2, 3 3 3, 1, 3 1 , 1, 1

Carry on the division although 3 is not divisible by 2.

Stop dividing when each quotient is 1

Therefore the LCM of 6, 8 and 12 =

Saturday, June 22, 2013

×

×

×

= 24


Common Factors 1. A common factor is a number which is a factor of two or more numbers For example :3 is a factor of 6 3 is a factor of 9 Therefore, 3 is a common factor of 6 and 9.

Saturday, June 22, 2013


Example : Find the common factors of (a) 8 and 12 .

(b)

4, 6 and 8

Solution ( a ) Factors of 8 :

1

22

4

8

Factors of 12 :

1

22

3

4 4

6

12

Therefore the common factors of 8 and 12 are 1, 2 and 4. Saturday, June 22, 2013


.

Solution ( b ) 1

2

4

Factors of 6 :

1

22

4

6

Factors of 8 :

1

2

4

8

Factors of 4 :

Therefore the common factors of 4, 6 and 8 are 1 and 2 Saturday, June 22, 2013


Test Yourself 1 The first three common multiples of 2, 3 and 4 are A

6, 12, 18

B

6, 18, 24

C

12, 18, 24

D

12, 24, 36

Saturday, June 22, 2013


Test Yourself 2 If 8 is a multiple of three numbers, what are those numbers? A

1, 2, 4

B

2, 3, 4

C

3, 4, 8

D

4, 5, 8

Saturday, June 22, 2013


Test Yourself 3 Which of the following is not common multiple of 8 and 9? A

36

B

72

C

144

D

216

Saturday, June 22, 2013


Test Yourself 4 Find the lowest common multiple of 3, 4 and 6 A

12

B

18

C

36

D

72

Saturday, June 22, 2013


TOPIC : NUMBER PATTERNS AND SEQUENCES Sub Topic : 2.8 Common Factors and Highest Common Factor (HCF) Learning Outcomes : i. Find common factors of two or three whole numbers. ii. Determine whether a number is a common factor of two or three given whole numbers. iii. Determine the HCF of two or three given numbers. Saturday, June 22, 2013


Common Factors 1. A common factor is a number which is a factor of two or more numbers For example :4 is a factor of 8 4 is a factor of 16 Therefore, 4 is a common factor of 8 and 16.

Saturday, June 22, 2013


Example : (a)

Find the common factors of 12 and 16

Solution Factors of 12 : Factors of 16 :

1

2 2

3

4

6

1

22

4

8

16

12

The common factors of 12 and 16 are 1, 2 and 4 Saturday, June 22, 2013


Example : (b) 21

Find the common factors of 9, 15 and 1

3

9

Factors of 15 :

1

33

5

15

Factors of 21 :

1

3

7

21

Factors of 9

:

Therefore the common factors of 9,15 and 21 are 1 and 3 Saturday, June 22, 2013


Highest Common Factor (HCF) 1. The Highest Common Factor (HCF) of several number is the largest common factor of those numbers 2. The Highest Common Factor (HCF) can be found by two methods: (i) Listing Method (ii) Using algorithm

Saturday, June 22, 2013


Example : Find the Highest Common Factor (HCF) of 18, 24 and 36.

Method (i) Method (ii)

Saturday, June 22, 2013


Listing down the multiples The factors of 18 :

1

2

33

6

9

18

The factors of 24 :

1

2

3

4

6

8

12 24

The factors of 36 :

1

2

33

4

6

9

12 18 36

The common factors of 18, 24 and 36 are 1, 2, 3 and 6 Therefore the highest common factor (HCF) of 18, 24 and 36 is 6. Saturday, June 22, 2013


Using algorithm 2 36, 18,24 3 18, 9, 12 6 , 3, 4

Division stops here because dividing when each quotient is 6, 3, and 4 do not have any common factors

Therefore the HCF of 18, 24 and 36 = Ă— = 6

Saturday, June 22, 2013


Test Yourself 1 Find all the common factors of 12 and 16. A

1,2 and 4

B

1, 2 and 6

C

1,2,3 and 4

D

1,2,4,and 8

Saturday, June 22, 2013


Test Yourself 2 60 is the lowest common multiple of ‌

A

15 and 24

B

12 and 24

C

12 and 15

D

12 and 20

Saturday, June 22, 2013


Test Yourself 3 The highest common factor (HCF) of 27, 45 and 54 is A

3

B

6

C

7

D

9

Saturday, June 22, 2013


Test Yourself 4 6 , 18 , 51 , 42 , 35 How many of the numbers above have a highest common factor of 6? A

2

B

3

C

4

D

5

Saturday, June 22, 2013


EXERCISE : NUMBER PATTERNS AND SEQUENCES (LCM)

Saturday, June 22, 2013


EXERCISE : NUMBER PATTERNS AND SEQUENCES (HCF)

Saturday, June 22, 2013


CREATED BY: EN SALLEHUDIN BIN TAHIR PN LATIFAH BT OTHMAN PN HASNAH BT OSMAN PN SITI KARTINI BT JAMAL CIK ZAINAB BT SAMAD CIK AIDAH MAHERAN BT MD AZNAN CIK MARYANI BT SIRASH

Saturday, June 22, 2013


Number patterns and sequences f1