The Difference Among LCM, LCD, GCD and GCF

LCM and LCD

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 and GCD

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

PCSR 2017 CIVIL SERVICE EXAM REVIEW GUIDE 1
Updated: April 25, 2017

PART I: MATHEMATICS

A. GCD

Videos

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

Articles

B. LCM

Videos

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

Article

C. Proper, Improper, and Mixed Form

D. More on LCM and GCD

PART II: ENGLISH

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
PART IV: TIPS AND TRICKS

Enjoy!

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

and

3, 6, 9, 12, 15, 18, 21, 24, 27, 30. » Read more

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