Lesson plans

HCF and LCM

1Class 5-Multiples &Factors, LCM &HCF

LESSON PLAN BREAK-UPLesson plan

Setting/time Slide # Topic

1 Classroom/30 mins Multiples

2 AV room/45 mins Composite and prime numbers

3 Class room/60 mins Divisibility rules, factorization/

4 AV room/45 mins Exponents and prime factorization

5 Class rooom/45 mins Class test

6 AV room/45 mins LCM

7 AV room/45 mins LCM

8 Class room/60 mins HCF

9 AV room/45 mins HCF

10 Class rooom/45 mins Class test

Content• Learning objectives• Multiples• Prime and composite numbers• Test of divisibility• Factors• Factorization and index notation• LCM

Prime FactorizationShort Division

• HCFPrime FactorizationShort DivisionFactor treeVenn Diagram

Class 5-Multiples &Factors, LCM &HCF 3

Learning ObjectivesThe student will be able to :• Differentiate between the terms

factors and multiples composite and prime numbers LCM and HCF

• Lists the multiples and factors of composite numbers• Express factors as index notations• Calculates the HCF and LCM of 2 or 3 digit numbers using

Number trees Prime factorization Long division method Venn Diagram

Class 5-Multiples &Factors, LCM &HCF 4

Multiples

• Multiples of a number can be made by multiplying the number by any whole number.

• 1X12=12• 2X12 = 24• 3 X12 =36• 4X12=4812, 24, 36, 48, 60, 72, 84,

96,108,120….are multiples of 12

1 x 10 = 10, 2 x 10 = 20, 3 x 10 = 30, 4 x 10 = 40, 5 x 10 = 50, 6 x 10 = 60, and so on ...

5Class 5-Multiples &Factors, LCM &HCF

Multiples

• 5 10 15 20 25 30 35 40 45 50 55

6Class 5-Multiples &Factors, LCM &HCF

A clock is set to ring at every 5th minute. Will it ring 55 minutes later?

Multiples• Is 12 a multiple of 3?

If you multiply 3 by 4 you get 12, so 12 is a multiple of 3.

• Is 15 a multiple of 3?3 x 5 = 15. So 15 is a multiple of 3, (and also of 5).

• Is 21 a multiple of 6?21 is not a multiple of 6 because you can't make 21 by multiplying 6 by any whole number.6 x 3 = 18 and 6 x 4 = 24 but there is no whole number between 3 and 4 that could give us an answer of 21.

What are the first five multiples of 13?

13 x 1 =13

13 x 2 = 26

13 x 3 = 39

13 x 4 = 52

13 x 5 = 65

13, 26, 39, 52, 6513, 26, 39, 52, 65

8Class 5-Multiples &Factors, LCM &HCF

Find the Missing Multiples

• 6, 12, 18, ____, ____

• ___, 6, 9, 12, ____, ____, 21

• ___, 24, 36, 48, 60, ____

24 30

3 15 18

12 72

9Class 5-Multiples &Factors, LCM &HCF

Composite and Prime numbers

10Class 5-Multiples &Factors, LCM &HCF

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100

Prime Numbers• A prime number is a positive integer that has exactly

two positive integer factors, 1 and itself.• For example, if we list the factors of 28, we have 1,

2, 4, 7, 14, and 28. That's six factors.• If we list the factors of 29, we only have 1 and 29.

That's two factors. So we say that 29 is a prime number, but 28 isn't.

11Class 5-Multiples &Factors, LCM &HCF

Composite Numbers• A Composite Number can be divided evenly by numbers

other than 1 or itself. • Example: is 6 a Prime Number or Composite Number?

• 6 can be divided evenly by 2, or by 3, as well as by 1 or 6:

• 6 = 1 × 66 = 2 × 3

• So 6 is a Composite Number

12Class 5-Multiples &Factors, LCM &HCF

Factors• Factors are the numbers you multiply

together to get a product or a factor is a number that exactly divides another number without leaving a remainder.

• 12 can be written as the product of 2 x 6 or 2 x 6 = 12

13Class 5-Multiples &Factors, LCM &HCF

2 and 6 are the factors of 12

12 is the multiple of its factors 2 and 6

FACTORSThe factors of 12 are:

– 1 x 12

– 2 x 6

– 3 x 4

– 4 x 3

– 6 x 2

– 12 x 1

• 12 can be divided evenly by 1, 2, 3, 4, 6 and 12:– 1 × 12 = 12

– 2 × 6 = 12

– 3 × 4 = 12

• So 12 is a Composite Number

• The factors of 12 are 1, 2, 3, 4, 6, and 12

Class 5-Multiples &Factors, LCM &HCF 14

Factors

15Class 5-Multiples &Factors, LCM &HCF

• For example, the product 24 has several factors.

• 24 = 1 x 24• 24 = 2 x 12• 24 = 3 x 8• 24 = 4 x 6• So, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

Divisibility rules

• A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8.• A number is divisible by 3 if the sum of the digits is divisible

by 3.• A number is divisible by 4 if the number formed by the last

two digits is divisible by 4.• A number is divisible by 5 if the last digit is either 0 or 5.• A number is divisible by 10 if the last digit is 0.• A number is divisible by 8 if the number formed by the last

three digits is divisible by 8.• A number is divisible by 9 if the sum of the digits is divisible

by 9.• A number is divisible by 6 if it is divisible by 2 AND it is

divisible by 3.

16Class 5-Multiples &Factors, LCM &HCF

Writing facors

The factors of 48 are

1 x 48 2 x 243 x 164 x 126 x 8

Another way of writing factors is:Write your first pair of factors with a reasonable space between them, then move on to the next pair until you have them all.This way, when you get to the 6,8 pair, you can stop because 7 is not a factor and you already have 8 in your list.

17Class 5-Multiples &Factors, LCM &HCF

Exponential Notation or Index Notation

• 4cm x 3cm= 12 cm square• When a number is multiplied by itself several

times, we express the product in the given form:

• 3x3=32 = three raised to the power 2• 4 x 4 x4 x 4 x 4= 4 5= 4 raised to the power 5• 8 7= 8 x 8 x 8 x 8 x 8 x 8 x 8• 2 x 2 x 2 x 4 x 4 = (2 x 2 x 2) x (3 x 3) =23 x 42

Class 5-Multiples &Factors, LCM &HCF 18

Exercise 11) Write in the exponential form.a) 5 x 5 x 5=b) 10 x 10 x 10 x 10=c) 6 x 6 x 6 x 6 x 6=d) 2 x 2 x 3 x 3=e) 8 x 8 x 8 x 4 x 4 x 4 x 4 1) Write in the product form.a) 8 7 =b) 6 3 x 11 4 =

Class 5-Multiples &Factors, LCM &HCF 19

Factorization & Exponents

• 60=1x60 60=2x30 60=3x20 60=4x15 60=5x12 60=6x10

20Class 5-Multiples &Factors, LCM &HCF

60

Factorization & Prime Factorization• The factor

pairs for 60 are• 60=1x60

60=2x30 60=3x20 60=4x15 60=5x12 60=6x10

60

2 30

Composite number

3 10

Composite number

2 5

60 is written as the product of its prime factors60 = 2 x2 x 3 x 5

FACTOR TREE

• 60=4x15 =2x2 x3 x5

60

4 15

3 5

22

Prime factorization through short division

60

30

15

2

2

3

5 51

The prime factors of 60 are

2x2x3x5

2, 3, and 5 are all prime numbers, so we have prime factored 60. All we have to do now is neaten our answer up a bit. It is customary to write prime factorizations in increasing order, that is with the smallest numbers first.

Prime Factorization

24Class 5-Multiples &Factors, LCM &HCF

So the prime factorization of 910 is 2x5x7x13

• Now let us try another example: 910

Least common Multiple-LCM• A cold drink truck visits Rita's neighbourhood

every 4 days and Amul ice cream truck visits her neighborhood every 5 days. For the month of June on which day will both the trucks visit on the same day?

25Class 5-Multiples &Factors, LCM &HCF

1 2 3 4 5 6 78 9 10 11 12 13 1415 16 17 18 19 20 2122 23 24 25 26 27 2829 30

Least common Multiple-LCM• In the given problem we have to first find the multiples of

both the numbers. • Cross out the multiples that are common. (20 and 40)• Which multiple is the least-20• Both the trucks will visit the neighbour hood on 20 June or

after 20 days.

Truck Days of visit

1 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44,...

2 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,...

26Class 5-Multiples &Factors, LCM &HCF

Exercise -Find the LCM of 18 and 24.

Multiples of 18 18, 36, 54, 72, 90, 108, 126, 144,…

Multiples of 24 24, 48, 72, 96, 120,144, ….

• Common multiples of 18 and 24 are 72 and 144 • The least common multiple of 18 and 24 is 72. • LCM = 72

Highest Common Factor-HCFFind the HCF of 60 and 72

,1815

2

60 ,72

30 ,36

5 ,6

2

3 ,1815

2

60 ,72

30 ,36

5 ,6

2

3

The common factors of 60 and 72 are 2 x 2 x 3The HCF of 60 and 72 =2x2x3=12

Uncommon factors

HCF by prime factorization

Factors of 60Factors of 72

LCM of 60 and 72

• To find the LCM of 60 and 72 we multiply all the factors.

• 2x2 x3x5x6 = 336

• So the HCF of 60 and 72 is 12 and

• LCM is 336

,1815

2

60 ,72

30 ,36

5 ,6

2

3

Find the HCF of 56 and 48– Prime Factor Tree for 56 • Prime Factor Tree for 48

56

2

2

28

14

2 7

56 is all the prime numbers 2 x 2 x 2 x 7 multiplied together

48

2

2

24

12

2 6

2 3

48 is the prime numbers 2 x 2 x 2 x 2 x 3 multiplied together

Look for common factors in both trees

Multiply them together =

x

x

48

2

2

24

12

2 6

2 3

56

2

2

28

14

2 7

2

2

2

88 is the biggest number that goes into both 56 and 48

So it is the Highest Common Factor

Finding the Highest Common Factor

HCF through Prime Factorization• The prime factors of : 56 = 2 x 2 x 2 x 7 48 = 2 x 2 x 2 x 2 x 3 The prime numbers that are common are: 2x2x 2= 8So the HCF of 56 and 48 is 8

HCF & LCM as a diagram

2

2 2

7

3

53

5

Write the common prime factors of both 504 and 700 here .The HCF =2X 2 X 7=28

Write the other PRIME FACTORS of 504 in the 504 circle

Write the other PRIME FACTORS of 700 in the 700 circle

504 700

The LCM is found by multiplying all the numbers from the circles

504 = 2 x 2 x 2 x 3 x 3 x 7700 = 2 x 2 x 5 x 5 x 7

The four different ways to find the HCF

504

2

2 2

7

3

53

5

700

,1815

2

60 ,72

30 ,36

5 ,6

2

3

The prime factors of : 56 = 2 x 2 x 2 x 7 48 = 2 x 2 x 2 x 2 x 3 The prime numbers that are common are: 2x2x 2= 8So the HCF of 56 and 48 is 8

x

x

48

2

2

24

12

2 6

2 3

56

2

2

28

14

2 7

2

2

2

8