Number Patterns and Sequences f1

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Wednesday, January 04, 2012

Sub Topic : 2.7 Common Multiples and Lowest CommonMultiple (LCM)

TOPIC : NUMBER PATTERNS AND SEQUENCES

Learning Outcomes : i. Find the common multiples of two or threewhole numbers.

ii. Determine whether a number is the commonmultiple of two or three given numbers.

iii. Determine the LCM of two or threegiven numbers.


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1

2

4

8

16


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Solution

Multiples 2 : 2 4 6 8

Multiples 3 :3 6 9 12 15 18

.

The first three common multiples of 2 and 3 are

6,12 and 18

6

1812

12

Find the first three common multiples of 2 and 3

10 12 14 16 18 20

18

6


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Lowest Common Multiple (LCM)

2. The lowest common multiple (LCM) can befound by two methods:

1. The lowest common multiple (LCM) of two orthree given numbers is the smallest commonmultiple of the given numbers.

(ii) Using algorithm

(i) Listing down the multiples


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Example :

Find the lowest common multiple 6, 8 and 12.

Method (i)

Method (ii)


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The common multiples of 6,8 and 12 are 24,48

Multiples of 8 : 8 16 24 32

Multiples of 12 : 12 24 36 48

.

Therefore the lowest common multiple (LCM) of 6,8and 12 is 24.

48

Multiples of 6 :6 12 18 48

4824

24

24

Listing down the multiples

24 30 36 42 48

40 48


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Using algorithm

6, 8, 122

3, 4, 6

2 3, 2, 3

2

3, 1, 33

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 = 24 =

2

2

2

3


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Common Factors

For example :3 is a factor of 6

3 is a factor of 9

1. A common factor is a number which is afactor of two or more numbers

Therefore, 3 is a common factor of 6 and 9.


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Example :Find the common factors of

(a) 8 and 12 (b) 4,6 and 8

Solution ( a )

Factors of 8 : 1 2 4 8

Factors of12

: 1 2 3 4 6 12

.

Therefore the common factors of 8 and 12 are 1,2

and 4.

1

1

2

2

4

4


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Solution ( b )



.

Therefore the common factors of 4,6 and 8 are 1 and 2

1

1 2

1

Factors of 4 :1 2 42

2

4

4

4


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Test Yourself 1

The first three common multiples of

2, 3 and 4 are

A 6,12,18

B 6,18,24

C12,

18,

24

D 12,24, 36


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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


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Test Yourself3

Which of the following is notcommon multiple of 8 and 9?

A 36

B 72

C144

D 216


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Test Yourself 4

Find the lowest common multipleof 3,4 and 6

A 12

B 18

C 36

D 72


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Sub Topic : 2.8 Common Factors and HighestCommon Factor (HCF)

TOPIC : NUMBER PATTERNS ANDSEQUENCES

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.


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Common Factors

For example :4 is a factor of 8

4 is a factor of 16

1. A common factor is a number which is afactor of two or more numbers

Therefore,4 is a common factor of 8 and 16.


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Solution

Factors of 12 :1

2 3 4

Factors of 16 :1 2 4 8 16

The common factors of 12 and 16 are

1,2 and 4

1

42

2

Example :

(a) Find the common factors of 12 and 16

6 124

1


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Factors of 15 : 1 3 5 15

Factors of 21 : 1 3 7 21

Therefore the common factors of 9,15 and 21 are 1 and 3

1

1 3

1

Factors of 9 :1 3 93

3

Example :

(b) Find the common factors of 9, 15 and 21


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Highest Common Factor (HCF)

2. The Highest Common Factor (HCF) can be found

by two methods:

1. The Highest Common Factor (HCF) of severalnumber is the largest common factor of those numbers

(ii) Using algorithm

(i) Listing Method


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Example :

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

Method (i)

Method (ii)


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The common factors of 18,24 and 36 are 1,2, 3 and 6

The factors of 24 : 1 2 3 4

The factors of 36 : 1 2 3

24

Therefore the highest common factor (HCF) of 18,24and 36 is 6.

6The factors of 18 :

1 2 3

6

6

1

1

2

Listing down the multiples

6 9 18

6 8

4 12

12

18 36961

2

2

3

3

3


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Using algorithm

36, 18,242

18, 9, 123

6 , 3, 4 Division stops here because

dividing when each quotient is6, 3, and 4 do not have any

common factors

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

2

3


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Test Yourself 1

Find all the common factors of

12 and 16.

A 1,2 and 4

B 1,2 and 6

C1,2,

3 and4

D 1,2,4,and 8


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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


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Test Yourself3

The highest common factor (HCF) of 27,45 and 54 is

A 3

B 6

C 7

D 9


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Test Yourself 4

How many of the numbers above have ahighest common factor of 6?

A 2

B 3

C 4

D 5

6,18,51,42, 35


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EXERCISE :

NUMBER PATTERNS

AND SEQUENCES

(LCM)


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EXERCISE :

NUMBER PATTERNS

AND SEQUENCES

(HCF)


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CREATED BY:

EN SALLEHUDIN BIN TAHIR

PN LATIFAH BT OTHMAN

PN HASNAH BT OSMANPN SITI KARTINI BT JAMAL

CIK ZAINAB BT SAMAD

CIK AIDAH MAHERAN BT MD AZNAN

CIK MARYANI BT SIRASH

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Number Patterns and Sequences f1