Lesson 3

Discover

 

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To add and subtract fractions you often have to find the lowest common multiple (LCM) to use as the lowest common denominator. In this section you will explore two different methods of determining the lowest common denominator for a set of rational denominators.

 

Try This 1

 

Method 1: Finding the LCM Using the Factored Form

1. Complete the following table. The first row has been completed to give you an idea of what is expected.
   
   
    

   Monomials	Factored Form	LCM
   x2 2x	x2 = x • x 2x = 2 • x
   10xy2 4x2y
   6x 4x2 x3
   8(a + b)3 4(a2 − b2)

Method 2: Finding the LCM Using Product and GCF

2.  
   1. Discover an alternate method of finding the LCM by completing the table and then answering the questions that follow. In the table, treat binomials as a single factor. Do not expand (multiply out) any of the factors. The first row has been completed to give you an idea of what is expected.
      
      
       

      Expressions	Product	GCF	LCM	GCF × LCM
      x2 2x		x2 = x • x 2x = 2 • x   GCF = x	x2 = x • x 2x = 2 • x	x • 2x2 = 2x3
      12xy 15y2
      (y + 2) 2(y + 2)
      (x + 3) (x − 3)

      
      
      
   2. Look at the rows of your completed table. Do you notice any patterns as you look horizontally across the rows? From these patterns do you see another method you could use to find the LCM?
      
      
3. What other previous math concepts have you learned that required you to work with lowest common multiples?
   
   
4. Why do you think it is important to be able to have different strategies to determine the LCM of a set of expressions?

Save your work in your course folder.

 

You will revisit these results later in the lesson.