This document discusses finding the least common multiple (LCM) of two or more numbers. It describes three methods for calculating the LCM: listing method, prime factorization/factor tree method, and continuous division/ladder method. Examples are provided to demonstrate each method. The lesson includes classroom activities where students practice finding LCMs in groups and assessments to check their understanding.

1. COMMON MULTIPLES
AND LCM OF TWO –
FOUR NUMBERS
-M5NS-Id-69.2-
LUISA F. GARCILLAN
Teacher 3- Math Teacher
Lapogan Integrated School
CLASSROOM OBSERVATION 1- MATHEMATICS 5

2. QUARTER 1
Lesson 12 :
A. Identify the multiples of a given number
B. Find the common multiples and LCM of
two - four numbers using continuous
division
C. Write the LCM of the given numbers using
the continuous division

3. Drill
Game – Skip Counting
Mechanics:
•Divide the pupils by two.
•Use the show me boards
•Flash the numbers on screen one at a time
and say, “Give the next three numbers in
the sequence.”

4. 0, 3, 6, 9, ___, ____, ___

5. 0, 3, 6, 9, 12, 15, 18

6. 0, 4, 8, 12,__, __, __

7. 0, 4, 8, 12,16, 20, 24

8. 0, 8, 16, 24,__, __, __

9. 0, 8, 16, 24,32, 40, 48

10. 0, 10, 20, 30,__, __, __

11. 0, 10, 20, 30,40, 50, 60

12. 0, 6, 12, 18,__, __, __

13. 0, 6, 12, 18, 24, 30, 36

14. 0, 7, 14, 21,__, __, __

15. 0, 7, 14, 21, 28, 35, 42

16. Review how to use the listing method to get the LCM of the given
number.
• List some multiplies of two given numbers.
• Write the common multiplies.
• The smallest common multiple is the LCM
3 6 9 12 15 21 24 27
4 8 12 16 20 24 28 32

17. Divide the class into 5 groups. Let each group get
the strip of cartolina and complete the given
chart. Get the LCM using Listing method.
Numbers LCM
1. 6, 10
2. 5, 7
3. 9, 12
4. 8, 40
5. 7, 28

21. Ask: What are the objects that
can be recycled? What do you
do in the used objects like
plastic bottles, used papers,
glass bottles etc.. What are the
good effects of recycling in our
environment?

22. Present this problem to the class.
-Bong Bong and Sarah
collected used plastic bottles
for recycling. They arranged
the bottles in boxes of 8 and
12. What is the least number of
bottles they gathered in all?

23. There are three ways of
getting the LCM the:
1.Listing Method
2.Prime Factorization/Factor Tree
3.ContinuousDivision/Ladder
Method

27. •What is the LCM of 8 and 12?
•Which method you think is
easier method?
•How did you get the LCM of 8
and 12 using the Continuous
Division Method?

28. •By getting the product of
all the prime divisor and
the last set of quotients
we get the Least Common
Multiples (LCM).

29. Group Activity

30. Find the least common multiples of the
following pairs of numbers.
Group 1 4, 6, and 8 -LISTING METHOD
Group 2 6 , 9 and 18 -PRIME FACTORIZATION
Group 3 3, 8 and 15 -CONTINUOUS DIVISION

31. •What is Least Common
Multiple (LCM) of two given
number?
•How do we find the Least
Common Multiple (LCM) of two
given numbers using
continuous division?

32. Least Common Multiple (LCM) is the smallest non-zero number
that is a multiple of all the numbers in the set.
Continuous division in finding the LCM is done following the
steps below:
Write the number horizontally and find a prime number that will
divide the numbers, if possible.
Divide by that prime number and write the quotients below the
dividends. Copy any numbers not divided below the dividend.
Continue the process until no two numbers have a common
prime divisor.
Multiply all the prime divisors and the last set of quotients to
get the LCM.

33. Assessment
Find the Least Common Multiple (LCM) of
the given pairs of numbers using any of the
three method.
1. 12 and 18
2. 11 and 99
3. 5, 10 and 30
4. 4, 5 and 16
5. 9, 54, and 90

34. Enrichment Activities:
Find the Least Common Multiple (LCM) of
the given pairs of numbers using the three
method.
1. 3 , 4, and 6
2. 2, 3, and 5
3. 4, 6, and 12
4. 3, 6, and 15

35. Thank you 
LUISA F. GARCILLAN
Teacher 3- Math Teacher
Lapogan Integrated School