Question

Note: This is NOT a question. This is a tutorial.

How to take the LCD/LCM of a rational expression/number? See comment below to see how!

Answer 1

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Answer 2

Taking the LCD/LCM only involves a few steps. For the simplicity of this tutorial, I'll use fractions. Suppose you are given:
\(\Large \frac{2}{3} + \frac{3}{4} + \frac{5}{6} + \frac{1}{9} + \frac{3}{8}\)

STEP 1: Express all your denominators as factors of prime numbers/expressions.

\(\Large \frac{2}{3} + \frac{3}{(2)(2)} + \frac{5}{(2)(3)} + \frac{1}{(3)(3)} + \frac{3}{(2)(2)(2)}\)

Step 2: List down your factored denominators.

Denominator 1: 3
Denominator 2: (2)(2)
Denominator 3: (2)(3)
Denominator 4: (3)(3)
Denominator 5: (2)(2)(2)

Step 3: Pick a number from this list. This becomes ONE of the factors of my LCD/LCM. Let's say I choose 3. My LCD/LCM now is \(3 \times a \times b \times c\) and so on, and so forth.

Step 4: Cancel ONE of that number (the number you chose in Step 3, which in our case it's 3) from EACH your denominators, if possible. And so, we'll cancel 3 from each of our denominators.

Denominator 1: \(\cancel{3}\)
Denominator 2:(2)(2) <---- no 3 so we don't cancel anything
Denominator 3: (2)\(\cancel{(3)}\)
Denominator 4: (3)\(\cancel{(3)}\) <-----note that we only cancel one 3
Denominator 5: (2)(2)(2) <----again no 3 so we don't cancel anything.

We repeat Step 3 and choose another number..this time I choose 2. So my LCD is now 3 x 2 but that's not yet finished. Again, we list down the remaining denominators.

Denominator 1: 1
Denominator 2: \(\cancel{(2)}\)(2) <----note that we only cancel one 2
Denominator 3: \(\cancel{(2)}\)(1)
Denominator 4: 3
Denominator 5: \(\cancel{(2)}\)(2)(2)

We again repeat Step 3. This time, I'll choose 3 again. So our LCD so far is 3 x 3 x 2. Now, we list te remaining denominators.

Denominator 1: 1
Denominator 2: 2
Denominator 3: 1
Denominator 4: \(\cancel{(3)}\)
Denominator 5: (2)(2)

Repeat Step 3 again. I'll choose 2 again this time. So our LCD is 3 x 3 x 2 x 2. List down the remaining denominators...

Denominator 1: 1
Denominator 2: \(\cancel{(2)}\)
Denominator 3: 1
Denominator 4: 1
Denominator 5: \(\cancel{(2)}\)(2)

Repeat Step 3. The only remaining number is 2 so that is the last input to out LCD. So the LCD of \(\Large \frac{2}{3} + \frac{3}{4} + \frac{5}{6} + \frac{1}{9} + \frac{3}{8}\) is 3 x 3 x 2 x 2 x 2 = 9 x 8 = 72 <---LCD

Answer 3

lol @jhonyy9 i had to type it :p =)))

Answer 4

yes is nice but very long

- is more easy if you check step by step like

- 1, for 3 and 4 you get 12
- so 12 is right for 6 too
- for 12 and 9 make 12=3*4 and 9=3*3 so than will be right 3*3*4 = 36
- than for 36 and 8 so 36=3*3*2*2 and 8=2*2*2 so than we get 3*3*2*2*2 =
=9*8=72

Answer 5

hmm i see...i admit that is faster...though i just want my tutorials to be beginner friendly haha you know...see it immediately...though that is a cool method too :D

Answer 6

A great tutorial! Perhaps using the calculator to do prime decomposition will be quicker.

Answer 7

haha thanks :) prime decomposition is fast...but i dont think it works on rational expressions? this does...i just used fractions for the simplicity of the method and to conserve latex haha

Answer 8

jhony's method too..i dont think works on rational expressions...does it @jhonyy9 ?

Answer 9

can you writing an example for what not is right ?

Answer 10

uhmm i dont know..i was just asking if your method works on rational expressions as well?

Answer 11

Haha, my method is almost exactly the same thing, here: http://puu.sh/slTq

Answer 12

maybe i'll write an example of a rational expression...

\(\Large \frac{4}{3x} + \frac{2x +5}{9x^2 + 18x + 9} + \frac{1}{9}\)

using my method..we list down the denominators in factored form...

\(\Large \frac{4}{(3)(x)} + \frac{2x +5}{(3)(3)(x+ 1)^2} + \frac{1}{(3)(3)}\)

List the denominators...

1st denom -> (3)(x)
2nd denom - > (3)(3)(x+1)^2
3rd denom -> (3)(3)

i'll choose 3.. cancel one 3 from each denom...

1st denom -> x
2nd denom -> 3(x+1)^2
3rd denom -> 3

i'll choose another 3..so my LCD so far is 9...cancel another 3 from the denoms...

1st denom -> x
2nd denom -> (x+1)^2
3rd denom -> 1

now i'll choose x (so LCD is now 9x)..cancel one x from each denom

1st denom -> 1
2nd denom -> (x+1)^2
3rd denom -> 1

sin (x+1)^2 is the only one left it automatically jons the LCD...and so..the combined LCD is 9x(x+1)^2

Answer 13

i cut it short of explanation hope it's still understandable

Answer 14

yes right too

Answer 15

http://puu.sh/slVK

:D

Answer 16

oh hmm guess that works there too

Answer 17

Good job! ;D

Answer 18

very nice..they should have a seperate section for tutorials, that way your work is more permanent...since many users may not see this post

Answer 19

or write up your tutorial somewhere and then you could just post the link to OS periodically to save you time

Answer 20

yeah i sometimes reference myself when answering questions :D as for the section...i just think a special status would be nice..because creating another section..we cant guarantee many people would see it either...maybe the admins can notice my works someday then they can think of something :D i think these have been brought up to the admin's attention already

Answer 21

:)

Answer 22

Nice new profile pic lgb, I always knew you were a girl!

Answer 23

kind of irrelevant to the thread but thanks :)

Answer 24

I agree with @dumbcow . Solving problems/ Answering questions is not like tutorial. Tutorials are more permanent. Sorry, that's irrelevant to the thread again :|

Answer 25

haha no...that's relevant bc it's about the tutorial..not abt the topic but what the heck haha...well i guess we can wait for the admin's decision on this..i mean if im the only one doing this i dont think ill get granted that request :p ahaha i dunno

Answer 26

This belongs in the Education Section.

Answer 27

we have that? o.O well it's still math :p i think this is what they call "gray area"

Answer 28

It should be created pretty soon actually. And you could declare your support for it in the next Open House

Answer 29

hmm sure :DDD the open house isnt going to be a thread in the os feedback again is it?

Answer 30

I don't know what they're going to do this time. @cshalvey would know better than I.

Answer 31

lgbasa is having graet tutorial classes nowa days..

Answer 32

haha thanks for that @shruti :) i try my best ^_^