Finding the Lowest Common DenominatorDate: 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 |
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