Of math is ppt

1. 05-03-2019 1
Highest Common Factors
& Lowest common
Multiples

2. NAME : SHUBHAM
JAIDEV
YASH
KISHAN
KANJI
KEVAL
CLASS : 1DC3
SUBJECT: MATHS

3. Multiples
 What is a multiple?
A number that may be divided by another number with no
remainder: 4, 6, and 12 are multiples of 2.
i.e. Multiples of 3 are all those numbers which appear in the
3 times table
 What are common multiples?
A common multiple of two or more numbers contains each
of them a number of times exactly, so, 24 is a common
multiple of 3 and 4.
i.e. A number which appears in the times tables of all the
numbers you are considering

4. Lowest Common Multiples
 What do we mean by ‘lowest common multiple’?
The smallest multiple that is exactly divisible by every
member of a set of numbers.
i.e. the lowest common multiple of 12 and 18 is 36
 How can we find lowest common multiples?
Write out the first few multiples of all the numbers in the data
set
Look for the lowest number that appears in all the lists

5. Finding Lowest common multiples
 Example:
Find the lowest common multiple of 3
and 7..
First few multiples of 3:
3 6 9 12 15 18 21
First few multiples of 7:
7 14 21
The lowest common multiple of 3 and 7 is:
21

6. LOWEST COMMON MULTIPLES
Find the lowest common multiples for the
following sets of numbers:
5 and 7
LCM = 35
6 and 10
LCM = 30
4, 6, and 12
LCM = 24

7. Factors
 What is a factor?
Factors of a number are those numbers that divide into it
exactly with no remainder.
I.e. the factors of 12 are 1, 12, 2, 6, 3 and 4.
 What are common factors?
Common factors are those factors which divide exactly into
all the numbers in the set.

8. Highest Common Factors
 What do we mean by highest common factor?
The highest common factor of a data set is the largest
number that divides exactly into all the numbers.
*How can we find highest common factors?
List the first few factors of each number
Look for the highest number that appears in all lists.

9. Finding Highest Common Factors
 Example
Find the highest common factor of 12 and 15. The factors of 12 are:
1, 2, 3, 4, 6, and 12
The factors of 15 are:
1, 3, 5, 15
So the highest common factor of 12 and 15 is
3

10. Highest common factors
 Find the highest common factors of the following sets
of numbers.
20 and 30
HCF = 10
14 and 12
HCF = 2
24, 36, and 42
HCF = 6
40, 45 and 50
HCF = 5

11. Prime Factors
 Sometimes we want to find just the prime factors of two
numbers.
What is a prime number?
A prime number only has 2 factors and those 2 factors
must be 1 and the number itself.
The first 5 prime numbers are:
2, 3, 5, 7, and 11

12. HCF and LCM by Fraction number
2/3,8/9,64/81,10/27 lcm(3,9,81,27)=81 lcm(2,8,64,10)=320
will find 2=2*1 hfc=hcf/lcm will find hcf 3=3*1
8=2*2*2 hfc=2/81 9=3*3
16=2*2*2*2 81=3*3*3*3
10=2*5 now find lcm of 2,8,64,10 27=3*3*3
HFC=2,8,16,10=2 2 2 8 64 10 hcf= 3
now find lcm of 3,9,81,27 2 1 4 32 5 lcm=lcm/hcf
3 3 9 81 27 2 1 2 16 5 lcm=320/3
3 1 3 27 9 2 1 1 8 5
3 1 1 9 3 2 1 1 4 5
3 1 1 3 1 2 1 1 2 5
1 1 1 1 5 1 1 1 5
1 1 1 1

13. HFC and LCM for Decimal number
1.75,5.6,7 lcm(1.75,5.6,7)=1.400
we will find lcm 175,56,7 only we will find hcf of 175,56,7
5 175 56 7 175=5*5*7
5 35 56 7 56=2*2*2*7
7 7 56 7 7=7*1
2 1 8 1 hcf(175,56,7)=7
2 1 4 1 hcf(1.75,5.6,7)=0.7
2 1 2 1
1 1 1
therefore lcm=(175,56,7)=5*5*7*2*2*2
=1400

14. Some Example of HCF
1 ) 513 , 1134 , 1215
513 = 3*3*3*19
1134= 2*3*3*3*3*7
1215= 3*3*3*3*3*5
 HCF = 3*3*3
= 27
2) 204 , 1109, 1445
204= 2*2*3*17
1109= 2*5*7*17
1445= 5*17*17
 HCF = 17

15. 3) 3556, 3444
3556 = 2*2*7*127
3444 = 2*2*3*7*41
 HCF = 2*2*7
= 28

16. Some Example of LCM
1. 72, 108, 210
72 = 2*2*2*3*3
108= 2*2*3*3*3
210= 2*3*5*7
LCM= 2*2*2*3*3*3*5*7
= 7560