This lesson plan outlines 10 lessons to teach students about multiples, factors, prime and composite numbers, divisibility rules, factorization, exponents, least common multiples (LCM), and highest common factors (HCF). Each lesson includes the topic, time, location, content overview, and learning objectives. Methods for finding LCM, HCF, prime factorization, and factorization are discussed. Practice problems are provided for students.

1. Lesson plans
HCF and LCM
By
Kavita Grover
1Class 5-Multiples &Factors, LCM &HCF

2. LESSON PLAN BREAK-UP
Lesson
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

3. Content
• Learning objectives
• Multiples
• Prime and composite numbers
• Test of divisibility
• Factors
• Factorization and index notation
• LCM
Prime Factorization
Short Division
• HCF
Prime Factorization
Short Division
Factor tree Class 5-Multiples &Factors, LCM &HCF 3

4. Learning Objectives
The 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

5. Multiples
• Multiples of a number
can be made by
multiplying the number
by any whole number.
• 1X12=12
• 2X12 = 24
• 3 X12 =36
• 4X12=48
12, 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

6. 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?

7. 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.

8. 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

9. 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

10. Composite and Prime numbers
10Class 5-Multiples &Factors, LCM &HCF
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

11. 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

12. 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 × 6
6 = 2 × 3
• So 6 is a Composite Number
12Class 5-Multiples &Factors, LCM &HCF

13. 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

14. FACTORS
The 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

15. 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

16. 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.
16
Class 5-Multiples &Factors,
LCM &HCF

17. Writing facors
The factors of 48 are
1 x 48
2 x 24
3 x 16
4 x 12
6 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

18. 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

19. Exercise 1
1) 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

20. Factorization & Exponents
• 60=1x60
60=2x30
60=3x20
60=4x15
60=5x12
60=6x10
20Class 5-Multiples &Factors, LCM &HCF
60

21. 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 factors
60 = 2 x2 x 3 x 5

22. FACTOR TREE
• 60=4x15
=2x2 x3 x5
60
4 15
3 5
22

23. Prime factorization through short
division
60
30
15
2
2
3
5 5
1
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.

24. Prime Factorization
24Class 5-Multiples &Factors, LCM &HCF
So the prime factorization of 910 is 2x5x7x13
• Now let us try another example: 910

25. 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 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30

26. 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

27. 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

28. Highest Common Factor-HCF
Find 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 3
The HCF of 60 and 72 =
2x2x3=12
Uncommon
factors

29. HCF by prime factorization
Factors of
60
Factors of
72

30. 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

31. 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

32. 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
8
8 is the biggest number that goes into both 56 and 48
So it is the Highest Common Factor
Finding the Highest Common Factor

33. 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= 8
So the HCF of 56 and 48 is 8

34. 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 7
700 = 2 x 2 x 5 x 5 x 7

35. 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= 8
So 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