Download Mathematics O Level: Secondary 1

Mathematics O Level: Secondary 1
LCM and HCF
Mark Lim
January 12, 2013
Mark Lim
Mathematics O Level: Secondary 1
Prime Numbers
• A prime number can only be divided evenly only by 1 and
itself.
• examples : 2, 3, 5, 7, 11, 13, 15, 17, 19
• 0 and 1 are neither Prime nor Composite numbers.
• 6 can be divided by 2 and 3.
• 6 can be divided by 6 and 1.
• 6 is a Composite number, and is not a prime number.
• 6 is composed of of 2 and 3.
Mark Lim
Mathematics O Level: Secondary 1
Prime Factors
• What are the prime factors of 12?
• Start from the smallest 2
• 12 divide by 2 = 6
• 6 divide by 3 = 3
• Since 3 is a prime number, we have the answer
Therefore, the prime factors of 12 = 2 × 2 × 3
Mark Lim
Mathematics O Level: Secondary 1
Prime Factors of 90
• What are the prime factors of 90?
• Break into 9 × 10
• Prime factors of 9 are 3 and 3
• Prime factors of 10 are 2 and 5
So prime factors of 90 are 3, 3, 2 and 5
Mark Lim
Mathematics O Level: Secondary 1
Multiples
7=7×1
14 = 7 × 2
21 = 7 × 3
28 = 7 × 4
• The word multiple comes from word ’multiply’.
• So, the multiples of 7 are 7, 14, 21, 28, and so on.
Mark Lim
Mathematics O Level: Secondary 1
Common Multiples
• Multiples that are common to two or more numbers are said
to be common multiples.
E.g. Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18,
Multiples of 3 are 3,6,9,12, 15, 18
• So, common multiples of 2 and 3 are 6, 12, and 18.
Mark Lim
Mathematics O Level: Secondary 1
Least Common Multiple(LCM)
• The smallest common multiple of two or more numbers is
called the lowest common multiple (LCM).
• Here,the multiples of 8 are 8, 16, 24, 32
• Here,the multiples of 3 are 3, 6, 9, 12, 15, 18, 21,24
Therefore, the LCM of 3 and 8 is 24 from above.
Mark Lim
Mathematics O Level: Secondary 1
Find the LCM of 30 and 45
List the prime factors
30 = 2 × 3 × 5
45 = 3 × 3 × 5
LCM = 2 × 3 × 3 × 5 = 90
Note: two occurences of 3, one occurences of 2 and one occurence
of 5.
Mark Lim
Mathematics O Level: Secondary 1
Using the algorithm to find LCM
Steps to find LCM
• 1. Divide by smallest prime number 3
• 2. If a number is not divisible,carry it down
• 3. Continue until only 1 remains
3|21, 63, 105
7|7, 21, 35
3|1, 3, 5
5|1, 1, 5
1, 1, 1
Hence LCM = 3x7x3x5 = 315
Mark Lim
Mathematics O Level: Secondary 1
Factors
• A whole number that divides exactly into another whole
number is called a factor of that number.So, 4 is a factor of
20 as it divides exactly into 20.
• If a number can be expressed as a product of two whole
numbers, then the whole numbers are called factors of that
number. So, the factors of 20 are 1, 2, 4, 5, 10 and 20.
20 = 1 × 20
20 = 4 × 5
20 = 2 × 10
Mark Lim
Mathematics O Level: Secondary 1
Common Factors
Factors that are common to two or more numbers are said to be
common factors.
4=1×4
=2×2
6=1×6
=2×3
so,the common factors of 4 and 6 is 2.
Mark Lim
Mathematics O Level: Secondary 1
Common Factors examples
Find the common factors of 10 and 30
10 = 1 × 10
=2×5
30 = 3 × 10
= 2 × 15 = 5 × 6
so,the common factors of 10 and 30 are 1,2,5 and 10.
Mark Lim
Mathematics O Level: Secondary 1
Highest Common Factor (HCF)
Sometimes it is called GCF( greatest common factor). The largest
common factor of two or more numbers is called the highest
common factor.
Find the HCF of 8 and 12.
8=1×8
=2×4
12 = 1 × 12
=2×6=3×4
1.First, break down the numbers into prime factors.
Factors of 8 are 1,2,4, and 8
Factors of 12 are 1,2,3,4,6 and 12. So common factors are: 1,2
and 4.
Therefore, the HCF is 4.
Mark Lim
Mathematics O Level: Secondary 1
Using the algorithm to find HCF
Steps to find HCF
• 1.Divide by smallest common prime number 2
• 2.Divide by common prime factor 3
• 3.Divide by common prime factor 3
• 4.Stop here as 1 is the only common factor
2|54, 90, 108
3|27, 45, 54
3|9, 15, 18
5|3, 5, 6
HCF = 2x3x3 = 18
Hence the HCF of 54, 90,and 108 is 8.
Mark Lim
Mathematics O Level: Secondary 1