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### 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

Associated Topics:
Middle School Fractions

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