# L C D

#### ob1

##### New member
Trying to help my sister with L C D and cant remember how will take all help thanks

#### tkhunny

##### Moderator
Staff member
You must remember Prime Factorization. Do you?

#### lookagain

##### Senior Member
ob1 said:
Trying to help my sister with L C D and cant remember how will take all help thanks
Can you determine the greatest common factor (g.c.f.) of two numbers?

If you can, the least common multiple (l.c.m.) is equal to the product of the two numbers,
divided by their greatest common factor.

Edit in place

#### Denis

##### Senior Member
AS far as I know, the "official/standard" names are:
GCD (Greatest Common Divisor)
LCM (Least Common Multiple)

A LCD is a Liquid Crystal Display!

#### mmm4444bot

##### Super Moderator
Staff member

When talking about adding fractions, we say, "You need a common denominator".

There are many common denominators; it's best to use the smallest one, to make the arithmetic simpler.

That number is the Least [of the] Common Denominator. In other words, we call it the LCD.

Denis is correct, also. When finding that number, we need to consider lists of multiples of each denominator, and look for values common to both lists. The LCD is the smallest multiple that's common to both lists".

So, that number is also called the Least [of the] Common Multiple. In other words, we also call it the LCM.

I think both descriptions are common.

lookagain gave the easy formula. Divide the product of the two denominators by their GCF.

tkhunny gave the way to their GCF: examine the prime factorizations of the two denominators.

EG:

Let's add the following two fractions.

1/90 + 1/140

We need a common denominator. Let's find the smallest one (the LCD).

Begin by examining the prime factorization of each denominator.

90 = 2 * 3^2 * 5

140 = 2^2 * 5 * 7

The factors common to both numbers are 2 and 5.

(2)(5) = 10, so 10 is the Greatest Common Factor (GCF) of 90 and 140.

Multiply the two numbers together, and divide by their GCF.

(90)(140)/10 = 1260

1260 is the Least Common Multiple (LCM) of 90 and 140; therefore, 1260 is the Least Common Denominator (LCD) for adding those two fractions.

1/90 + 1/140

Switch to the common denominator:

14/1260 + 9/1260

Now we can add them because the denomiators are the same:

(14 + 9)/1260 = 23/1260

We just used the LCD to add 1/90 to 1/140. Their sum is 23/1260.

#### lookagain

##### Senior Member
Denis said:
AS far as I know, the "official/standard" names are:
GCD (Greatest Common Divisor)
LCM (Least Common Multiple)

A LCD is a Liquid Crystal Display!

The "GCD" can be the "greatest common divisor," but "GCF" is referred to as the "greatest common factor,"
and "GCF" I have found is more commonly used than "GCD."

Another point of view:

http://en.wikipedia.org/wiki/Greatest_common_factor

------------------------------------------------------------------------------------------------------------------------------------

The "LCM" can be the "least common multiple," but when you are referring to the denominators,
it is more specifically the "LCD," the "least common denominator." If you are finding the LCD of two or more
fractions, then you are finding the LCM of their denominators. But if you are finding the LCM of two or more
numbers, then you are not necessarily even working with fractions.

Another point of view:

http://en.wikipedia.org/wiki/Least_common_denominator

#### Denis

##### Senior Member
Ya, that's all nice...but not my point...

Searches by "learning students" will lead to sites like:
http://www.tigernt.com/math/math5gl.php

Programming languages (at least the ones I'm familiar with) all use GCD and LCM as commands.

I'm not "against" using others, but why confuse the learning student...

Anyway, it all matters little in the long-run; once the student "grasps/sees"
what's going on, the "name" matters none :idea:

#### lookagain

##### Senior Member
Denis said:
I'm not "against" using others, but why confuse the learning student...
There is **no** confusing the student by me. The student can stick
with the abbreviations I gave as they are more standard than yours.
And, the student should be familiar with the major variations of
their abbreviations, as they are given differently in courses/texts.

What they're called in your programming languages are irrelevant
to what the students should know them as in their arithmetic studies.

#### Denis

##### Senior Member
Ya, you're right, never wrong, as usual. I resign from this thread.

Post Deleted

#### lookagain

##### Senior Member
Denis said:
Ya, you're right, never wrong, as usual. I resign from this thread.
You are mistaken about me never being wrong. In the span of my education from kindergarten
all the way through graduate courses in mathematics, I have been wrong a grand total of at
least one time.

#### Denis

##### Senior Member
lookagain said:
....I have been wrong a grand total of at
least one time.
....which was calling a LCM a LCD :wink:

#### mmm4444bot

##### Super Moderator
Staff member
Denis said:
the "official/standard" names are:

GCD (Greatest Common Divisor)
Denis said:
Searches by "learning students" will lead to sites like:

[attachment=0:1wlqyrld]standficial no men clature.JPG[/attachment:1wlqyrld]
Heh, heh, heh.

The rate at which ambiguous information is published on the Internet will most likely always exceed the capacity of humans to correct.

I'm a strong believer that "learning" math students should rely mainly on bonafide textbooks and classroom instruction.

We all live in a big world; many different people make it go 'round and 'round. It's obvious to me that different people communicate differently. (Most people around me from day to day seem to generally not understand me when I speak!)

As long as two people each understand what the other means, successful interpersonal communication takes place -- despite the language.

Reaching this mutual understanding from day to day seems to be a lifelong, continuous learning process.

And now for something completely different: bowling with cats!

(It's coming, Denis. Hallow oww oowww oooowwwwwwwww weeeeeen)

http://www.bravozulu.com/content/includes/cat.swf

#### mmm4444bot

##### Super Moderator
Staff member

For me, knocking over cats with a bowling ball is eerily satisfying. :twisted:

And that's what the Internet is really all about, yes ?

(Double-click image to expand, if needed.)

[attachment=0:2u6jz1pw]Bowling with Cats.JPG[/attachment:2u6jz1pw]