Browse Tag: least common multiple

Review for August 2019 has already started

After a one-month break, we have already started our review series for the month of August 2019. The date of the examination will be on August 7, 2019. If you wish to follow our review series (I suggest you do), please like and then follow the Philippine Civil  Service Exam Reviewer Facebook page. Every week, we post Math, English, and Clerical tutorials and practice questions. For the first week our topics are LCM, GCD, Subject Verb agreement. You may download the review outline here.

We have already posted new video tutorials in Filipino on LCM and GCD on the Sipnayan Youtube channel.

Greatest Common Divisor/Greatest Common Factor

Continue Reading

The Difference Among LCM, LCD, GCD and GCF


LCM means Least Common Multiple. Multiple in this context is used for integers. LCD, on the other hand, means Least Common Denominator. As we know, denominator is used in fractions.

So, in 1/3 and 1/4, should we say, LCM or LCD?

CORRECT STATEMENT: LCM of 3 and 4 (multiple is used for integers).
CORRECT STATEMENT: LCD of 1/3 and 1/4 (denominator is used for fractions).

It is INCORRECT to say LCM of 1/3 and 1/4.

Notice that the LCM of 3 and 4 and the LCD of 1/3 and 1/4 is 12. That’s why most people use them interchangeably.


GCF means Greatest Common Factor

A factor of an integer is an integer that can be multiplied with another integer to get the given integer. For example, 3 is a factor of 6 because 3 x 2 = 6.

A divisor of an integer is an integer that divides that integer (without a remainder). For example, 3 is a divisor of 6 because 6/3 = 2, which is an integer.

Basically, factors and divisors have the same meaning when it comes to integers. Factor, however, is the term used in multiplication, while divisor is the term used for division. Here are some examples.

Positive factors of 12 are 1, 2, 4, 6, 12.
Positive divisors of 12 are 1, 2, 4, 6, 12.

GCF and GCD have the same meaning and will give the same values.

PCSR Civil Service Exam Review Guide 1

Updated: April 25, 2017




Lesson 1: Understanding Common Divisors
Lesson 2: Common Divisors and Greatest Common Divisor
Lesson 3: Exercises on Getting the GCD
Lesson 4: Getting the GCD by Prime Factorization
Lesson 5: GCD and Reducing Fractions to Lowest Terms




Lesson 1: Least Common Multiple Part 1
Lesson 2: Least Common Multiple Part 2
Lesson 3: Least Common Multiple Part 3


C. Proper, Improper, and Mixed Form

D. More on LCM and GCD


A. Vocabulary

Tip: Try to memorize the words and use it in your own words.

B. Grammar

Lesson 1: Verb and Tenses: An Introduction
Lesson 2: The Subject-Verb Agreement Rules Part 1
Lesson 3: The Subject-Verb Agreement Rules Part 2
Lesson 4: Subject-Verb Agreement

C. Spelling

Civil Service Review Spelling Quiz 1

Part III: CLERICAL Operations (Subprofessional)

Alphabetizing Rules Part 1


The Least Common Multiple Quiz

After taking the Greatest Common Factor Quiz, let me give you a Least Common Multiple Quiz, a topic that is quite related to greatest common factor. In case you missed it, I have already explained the concept of Least Common Multiple (LCM), you can read it before taking the quiz. The LCM is needed to add or subtract fractions, particularly dissimilar fractions.

The Least Common Multiple Quiz

Find the least common factor of the following numbers.

1.) 6 and 8
[toggle title=”Answer”]24[/toggle]

2.) 5 and 4  Continue Reading

Tagalog Video: The Concept of Least Common Multiple

I am planning to include videos of explanation of mathematical concepts in this blog and below is my first trial video. The explanation in the video is mostly Filipino (Tagalog) and sometimes English. This video discusses the concept of least common multiple which is used in addition of fractions.

I hope you learn something from here. Please feel free to use the comment box.  🙂

Note: In 4:49, I said that the fraction will become larger. Actually, the value of the fraction does not change. It is the number in the numerator and the denominator that becomes larger.

How to Add Fractions

Fractions whose denominators are the same are called similar fractions. Fractions that are not similar are called dissimilar fractions. Hence, the fractions \frac{1}{8}, \frac{3}{8}, and \frac{5}{8} are similar fractions, while the fractions \frac{2}{3} and \frac{1}{2} are dissimilar fractions. In this post, we are going to learn how to add fractions. 

How to Add Similar Fractions

Adding similar fractions is very easy.  In adding similar fractions, you just add the numerator and copy the denominator.  Here are a few examples.

Example 1

\displaystyle \frac{1}{5} + \frac{2}{5} = \frac{1 + 2}{5} = \frac{3}{5}

Example 2

\displaystyle \frac{1}{8} + \frac{2}{8} + \frac{4}{8} = \frac{1 + 2 + 4}{8} = \frac{7}{8} Continue Reading

How to Get the Least Common Multiple of Numbers

In mathematics, a multiple is a product of any number and an integer. The numbers 16, -48 and 72 are multiples of 8 because 8 x 2 = 16, 8 x -3 = -48 and 8 x 9 = 72. Similarly, the first five positive  multiples of 7 are the following:

7, 14, 21, 28, 35.

In this post, we will particularly talk about positive integers and positive multiples.  This is in preparation for the discussions on addition and subtraction of fractions.

We can always find a common multiple given two or more numbers. For example, if we list all the positive multiples of 2 and 3, we have

2, 4, 6, 8, 10, 12, 14, 16, 18, 20


3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Continue Reading