This document discusses finding the least common multiple (LCM) of sets of numbers. It begins with examples of finding the LCM of various number pairs and sets. These examples illustrate finding the prime factors of each number and identifying the smallest number that is a multiple of all numbers as their LCM. The document then provides practice problems for readers to identify the LCM of additional number sets. It concludes by recapping that the LCM is the smallest number that is divisible by all numbers in the set.

1. LEAST
COMMON
MULTIPLE

2. EXPECTATIONS
This lesson will help you to:
use the concept of finding prime factors in
identifying the least common multiple of a set
numbers; and
solve problems using the concept of least common
multiple.

3. PREPARATORY ACTIVITY
Find the number, which when multiplied by the given
number, will result in the encircled number on the right. The
first number is done for your reference.
Given Expected Result
1. 3 x 4
4 x 3
12
The numbers that you need to multiply is 4 for
the first given, then 3 for the second given.
Both will result in 12.

4. PREPARATORY ACTIVITY
Now, try the remaining items.
Given Expected Result
2. 5 x ____
3 x ____
3. 4 x ____
5 x ____
15
20
3
5
5
4

5. PREPARATORY ACTIVITY
Now, try the remaining items.
Given Expected Result
4. 6 x ____
8 x ____
12 x ____
5. 6 x ____
9 x ____
15 x ____
24
90
4
3
15
10
2
6

6. EXLORATORY ACTIVITY
Let us consider the list of numbers in the box below:
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
X X X
X X X
X X X
X X X
X X X
L
C
M
Least Common Multiple

7. Example 1:
a. List down 6 consecutive natural numbers which
are multiples of 7 starting from number 21.
b. List down 6 consecutive natural numbers which
are multiples of 8 starting from number 16.
Answer:
a. Since the numbers will start from 21, we have
the following as multiples of 7:
b. Since the numbers will start from 16, the
multiples of 8 are as follows:
21 28 35 42 49 and 56
16 24 32 40 48 and 56

8. Example 2:
Consider the set of numbers below:
Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Multiples of 5:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
a. What are the common multiples of 5 and 3?
b. What is the least common multiple of 5 and 3?

9. Answer:
a. The numbers 15 and 30 are the common multiples
of 5 and 3.
b. Since the smallest of the common multiples of 5
and 3 is 15, we can conclude that the LCM of 5
and 3 is 15.

10. Example 2:
Consider the set of numbers below:
Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Multiples of 5:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
a. What are the common multiples of 5 and 3?
b. What is the least common multiple of 5 and 3?

11. Example 3:
Find the least common multiple of the
numbers 6 and 8.
Answer:
Multiples of 6:
6, 12, 18, 24, 30
Multiples of 6:
8, 16, 24, 32, 40

12. Example 4:
Find the least common multiple of the
numbers 3, 4, and 6.
Answer:
Since there are three numbers involved, make
sure that all the numbers are considered.
Multiples of 3:
Multiples of 4:
Multiples of 6:
3, 6, 9, 12, 15, 18, 24, 27, 30
4, 8, 12, 16, 20, 24, 28, 32, 36, 40
6, 12, 18, 24, 30, 36, 42, 48, 54, 60

13. Example 5:
Find the least common multiple of 12 and 15.
Solution:
Find the prime factors.
Multiples of 12: 2, 2, 3
Multiples of 15: 3, 5
List down the numbers that are common to
both numbers, then copy those which are not
common, Thus:
3 (common to both numbers)
2, 2, and 3 (not common to both numbers)

14. Example 5:
Find the least common multiple of 12 and 15.
Solution:
Multiply them:
3 x 2 x 2 x 5 = 60
The product of these factors is the LCM of
the given numbers.
Therefore the LCM is 60.

15. Example 6:
Elisa loves to swim and dance. She started
swimming and dancing on June 3, 2012. From then on,
she swims every fourth day and dances every third
day. On what day will she he able to do both
activities?
Answer:
The least common multiple of 3 and 4 is 12.
This means that after 12 days, Elisa will do both
swimming and dancing again. Therefore, we get the
answer June 15, 2012 after adding 12 days since she
started swimming and dancing on June 3.

16. Example 7:
Lance is a box company. There are three
kinds of boxes they produce every day. The first
one is 10 inches tall, the second is 15 inches tall
while the third one is 21 inches tall. When you stack
the 3 boxes, what is the shortest height at which
they will have the same height?
Answer:
By getting their least common multiple we
could come up with the idea of their shortest
common height. Two hundred ten inches is the least
common multiple. Therefore, the shortest height is
210 inches.

17. LET’S PRACTICE
Identify the least common multiple (LCM) of
the following numbers:
1. 12 and 15 ______
2. 13 and 26 ______
3. 30 and 45 ______
4. 45 and 60 ______
5. 55 and 75 ______
60
26
90
180
825

18. LET’S PRACTICE
Identify the least common multiple (LCM) of
the following numbers:
6. 40 and 60 ______
7. 25, 35, and 45 ______
8. 24, 28, and 36 ______
9. 48, 72, and 98 ______
10. 60, 78, and 108 ______
120
1 575
504
7 056
7 060

19. RECAP
 If two or more numbers have the same
multiples, we call those numbers common
multiples.
 The Least Common Multiple (LCM) of
two or more numbers is the smallest
number that is divisible to the given set
of natural numbers.

20. EXERCISES
EASY & AVERAGE (PAGE 263)
Find the least common multiple of the
following numbers:
Example:
2 and 11
Multiples of 2:
2, 4, 6, 8, 10,12, 14, 16, 18, 20, 22
Multiples of 11:
11, 22

21. EXCERCISES
Find the least common multiple of the
following numbers: (1-10 only)
1. 12 and 24 ______
2. 8 and 24 ______
3. 12 and 15 ______
4. 3 and 11 ______
5. 12 and 16 ______
24
24
60
33
48

22. EXCERCISES
Find the least common multiple of the
following numbers: (1-10 only)
6. 6 and 15 ______
7. 16 and 24 ______
8. 25 and 35 ______
9. 50 and 75 ______
10. 45 and 80 ______
30
48
175
150
720

23. Thank
You!