Finding the Lowest Common Denominator

Date: 12/11/95 at 18:22:49
From: Anonymous
Subject: fractions(lcd)

What is the most efficient way to find the lcd (lowest common 
denominator).

Date: 5/31/96 at 15:27:52
From: Doctor Gary
Subject: Re: fractions(lcd)

  Step 1:  Fully factor all the terms for which you want to 
find the lowest common denominator (also called the "least 
common multiple).   

   Very important Note:  If a factor is repeated, be sure to 
write it out as many times as it is used.

  Step 2:  Multiply all the factors by one another (using 
those which are factors in more than one term only once).

  Example:  find LCD for 8, 12 and 18

 Step 1:  Fully factor each term

     8  =  2 x 2 x 2

    12  =  2 x 2 x 3

    18  =  2 x 3 x 3

 Step 2:  Multiply

    Multiplying all the factors by one another would give us:

    (2 x 2 x 2) (2 x 2 x 3) (2 x 3 x 3)

   Remember, however, that we don't re-use factors that are 
in more than one term.  Consequently, we need not multiply by 
either of the two 2's which are factors of 12, or the 2 which 
is a factor of 18, because these factors appear in more than 
one term.  Similarly, one of the 3s that are factors of 18
appears as a factor of 12, so we won't use that either.

  Our LCD is 2 x 2 x 2 x 3 x 3  =  72

 NOTE:  the 2 that is a factor of all three terms is called 
the greatest common factor.    

-Doctor Gary,  The Math Forum