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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 )
Factors of 6 : 1 2 4 6
Factors of 8 : 1 2 4 8
.
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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