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Department of Education
Region III
DIVISON OF MABALACAT CITY
Name: __________________________________ Grade & Section: ________________
School: ____________________________________________ Date: ________________
LEARNING ACTIVITY SHEET
Math 5 – Finding GCF and LCM
I. Introduction
Factoring is a useful skill in real life. It is commonly applied in dividing
something into equal prices, exchanging money, comparing prices,
exchanging money and even in making calculations during travel.
This Learning activity sheet, provided you activities develop your skills in
finding the common factors and Greatest Common Factors (GCF), common
multiples and Least Common Multiples (LCM) of 2-4 numbers using
continuous division. Real-life word problems involving GCF and LCM were
also given to support and understand deeper the concept of this lesson.
Hoping that you will find out for yourself that Mathematics is not difficult as
some learners think it is. Enjoy learning!
II. Learning Competency
This Learning Activity Sheets was designed and written with you in mind. It
is here to help you find the common factors, GCF, common multiples and
LCM of 2-4 numbers using continuous division (M5NS- Ie-70.2)
III. Objectives
After going through this Learning Activity Sheets, you are expected to:
1. find the common factors, GCF, common multiples and LCM of 2-4
numbers using continuous division
2. write the common factors and multiples of 2-3 numbers
3. work independently.
1
IV. Discussion
Problem:
Lani wants to put 16 big bottles of sanitizers and 20 small
bottles of sanitizers for the front liners into same boxes so that
each box has the same number of big and small
bottles of sanitizer.
How many boxes will she need?
To find the greatest number of boxes, find the greatest common of
factor 16 and 20.
How?
To get the factors of 16 and 20, think of the following mathematical sentence.
16 20
1 x 16 =16 1 x 20 = 20
2 x 8 = 16 2 x 10 = 20
4 x 4 = 16 4 x 5 = 20
Factors of 16 Factors of 20 are
are 1,2,4,8 and 1,2,4,5,10, and 20
16
16 1 2 4 8 16
20 1 2 4 5 10 20
From the list of factors, the common factors of 16 and 20 are:1, 2 and 4.
The GCF is 4.
So, Lani needs 4 boxes with the same number of big and small bottles of
sanitizer.
By using the Continuous Division which is also known as
Ladder Method
Follow these steps.
Step 1: Write the number in horizontal line.
16 20 What prime number can divide 16 and 20? (2)
2
Step 2: Write the common prime factor to the left side of 16 and 20 and write
the quotient below the numbers. Repeat the process until there is no
common prime factor. (divisor)
2 16 20 both are divisible by 2
2 8 10
4 5
Step 3: Multiply all common prime factors (divisor).
We have 2 x 2 = 4
Therefore, GCF is 4
So, Lani needs 4 boxes with the same number of big and small
bottles of sanitizer.
Another Example: What is the GCF of 12, 18, and 36
Step1 12 18 36 Arrange the given number horizontally.
2 12 18 36 Write the common prime divisor at the
left hand side and the quotients
6 9 12 below the number
Step 2 2 12 18 36 Repeat the process until there is no
common prime numbers
3 6 9 12
2 3 4
Step 3 2 x 3 = 6 Multiply all the common divisor
The GCF of 12, 18, and 36 is 6.
Finding the Least Common Multiples
At the Library, two table clocks ring and alarm at
different times. Table clock A rings alarm at 3 hours
while table clock B ring every 4 hours. If the clocks ring
at the same time at noon, at what time will they ring at
the same time again?
To find the answer, solve for the Least Common Multiple
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To find the answer, when the clocks ring at the same time at noon, and
what time will they ring at the same time again, solve for the Least
Common Multiple.
The Least Common Multiple (LCM) of two or more non zero whole
numbers is the smallest number which is a multiple of the given
set of numbers.
List the multiples for each interval:
Clock A: 3 = 3, 6, 9, 12, 15, 18, 21, 24 ……
Clock B: 4 = 4, 8, 12, 16, 20, 24, 28……
Take the common multiples: 12, 24; 12 is the LCM
This means that the clocks ring at the same time every after 12 hours
Therefore, if the clocks rang at the same time at 12noon.
they will ring at the same time again at 12midnight.
Here is other method to find the LCM of a given set of numbers using the
Continuous Division.
Example: 36 and 54
36 54
2 36 36 ÷ 2 = 18 2 54 54 ÷ 2 = 27
2
2 18 18 ÷ 2 = 9 3 27 27 ÷ 3 = 9
2
3 9 9 ÷ 3 = 3 3 9 9 ÷ 3 = 3
3
3 3 3 ÷ 3 = 1 3 3 3 ÷ 3 = 1
3
1 1
36 = 2 x 2 x 3 x 3 54 = 2 x 3 x 3 x 3
36 = 2 x 2 x 3 x 3
54 = 2 x 3 x 3 x 3
Therefore LCM of 36 and 54 is 2 x 2 x 3 x 3 x 3 = 144
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