Your Algebra Homework Can Now Be Easier Than Ever!

Constructing-a-Least-Common-Denominator

Constructing a Least Common Denominator (LCD)
When Adding or Subtracting Fractions with Unlike Denominators

When adding or subtracting fractions we need both fractions to have the same denominator. When this happens
we say that the fractions have Like Denominators . In order to keep our computations to a minimum we will be
using the Least Common Denominator (LCD) as our like (or common) denominators.

There are three cases to consider:
Case 1: One denominator is a multiple of the other denominator.
Case 2: The two denominators are relatively prime ( equivalently , GCF = 1)
Case 3: The two denominators have a GCF ≠ 1.


Case 1: One denominator is a multiple of the other denominator.
Construction of the LCD : Use the larger of the two denominators as your LCD.

Examples:

12 is a multiple of 4. 24 is a multiple of 2. 60 is a multiple of 5. 24 is a multiple of 3. 75 is a multiple of 15.
Use LCD = 12. Use LCD = 24. Use LCD = 60. Use LCD = 24. Use LCD = 75.

Case 2: The two denominators are relatively prime (equivalently, GCF = 1)
Construction of the LCD: Multiply the two denominators together to get your LCD.

Examples:

GCF(15, 4) = 1,
and 15 × 4 = 60.
GCF(3, 7) = 1,
and 3 × 7 = 21.
GCF(7, 6) = 1,
and 7 × 6 = 42.
GCF(9, 4) = 1,
and 9 × 4 = 36.
GCF(21, 2) = 1,
and 21 × 2 = 42.
Use LCD = 60. Use LCD = 21. Use LCD = 42. Use LCD = 36. Use LCD = 42.

Case 3: The two denominators have a GCF other than 1.
Construction of the LCD: Use the prime factorization method (explained in class) to construct the LCD.

Examples:

10 = 2 • 5 and
25 = 52 , so the
LCD = 2•52
9 = 32 and
15 = 3• 5, so the
LCD = 32 •5
18 = 2 •32 and
12 = 22 •3 , so the
LCD = 22•32
14 = 2•7 and
21 = 3 •7, so the
LCD = 2 •3• 7
22 = 2• 11 and
33 = 3• 11, so the
LCD = 2 •3• 11
Use LCD = 50. Use LCD = 45. Use LCD = 36. Use LCD = 42. Use LCD = 66.

Practice Identifying the
Least Common Denominator (LCD)


The Least Common Denominator (LCD) is the Least Common Multiple ( LCM ) of the denominators.

In cases 1 and 2, the LCD, if computed, would be the simpler forms described in the handout. Case 3 is the
only case that actually requires an official computation for the LCD.

From before:
Case 1:
One denominator is a multiple of the other denominator.
1. Use the larger of the two denominators as your LCD.
Case 2:
The two denominators are relatively prime (equivalently, GCF = 1)
1. Multiply the two denominators together to get your LCD.
Case 3:
The two denominators have a GCF ≠ 1.
1. Use the Prime Factorization Method to construct the LCD.


Indicate the cases to which the denominators belong. Then, indicate the LCD.
•Do your scratch work for Case 3 on another sheet of paper.





Solutions :

1.) Case 3; LCD = 42 2.) Case 2; LCD = 77 3.) Case 3; LCD = 150 4.) Case 3; LCD = 24
5.) Case 1; LCD = 70 6.) Case 2; LCD = 60 7.) Case 3; LCD = 400 8.) Case 2; LCD = 120

Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of November 2nd you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:



Algebra Helper can solve problems in all the following areas:

  • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
  • factoring and expanding expressions
  • finding LCM and GCF
  • (simplifying, rationalizing complex denominators...)
  • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
  • solving a system of two and three linear equations (including Cramer's rule)
  • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
  • graphing general functions
  • operations with functions (composition, inverse, range, domain...)
  • simplifying logarithms
  • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
  • arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath
Check out our demo!
 
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
 
 
Sofmath
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805
 

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2024, Algebra-Answer.Com.  All rights reserved.