Least common denominator

Least common denominator   

Hello ScienceBee, here we are going to learn about the least common denominator. 
 

 

What is least common denominator?   

The lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions. 

Video: Teaching Kids LCM & GCF With the Ladder Method
 
The lowest common denominator of a set of fractions is the lowest number that is a multiple of all the denominators: their lowest common multiple.
The product of the denominators is always a common denominator, as in: 
but it's not always the lowest common denominator, as in: 
Here, 36 is the least common multiple of 12 and 18. Their product, 216, is also a common denominator, but calculating with that denominator involves larger numbers: 
.
With variables rather than numbers, the same principles apply:

 

What's the role of LCD in arithmetic and algebra

The same fraction can be expressed in many different forms. As long as the ratio between numerator and denominator is the same, the fractions represent the same number. For example:
because they are all multiplied by 1 written as a fraction:
It is usually easiest to add, subtract, or compare fractions when each is expressed with the same denominator, called a "common denominator". For example, the numerators of fractions with common denominators can simply be added, such that and that , since each fraction has the common denominator 12. Without computing a common denominator, it is not obvious as to what equals, or whether is greater than or less than . Any common denominator will do, but usually the lowest common denominator is desirable because it makes the rest of the calculation as simple as possible.

 

What is least common denominator?   

This video discusses the least common denominator.

 

What is least common denominator for fractions?   

This video shows how to find the least common denominator for fractions.

 

Exercises to show to how to find the least common multiple   

This video shows how to find the least common multiple.

 

Simplifying a rational expression using the least common denominator?   

 This video shows how to simplify a rational expression using the least common denominator. 

 

Factoring Trinomials to find LCD of Rational Expressions 5.2?   

This video shows how to factor Trinomials to find LCD of Rational Expressions.

 

Let's Review

  1. The lowest common denominator or least common denominator (abbreviated LCD) is the ____ common multiple of the denominators of a set of fractions.
  2. The lowest common denominator of a set of fractions is the lowest number that is a ____ of all the denominators: their lowest common multiple.

     

    Answer

    1. The lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions.
    2. The lowest common denominator of a set of fractions is the lowest number that is a multiple of all the denominators: their lowest common multiple.

     

    Test Your Knowledge

     

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