Here are the steps required for Finding the Least Common Denominator (LCD):

Step 1: Factor each denominator into prime factors.
Step 2: Write the first denominator down. Then look at each additional denominator and write down any new factors that were not in the first denominator. If the same factor appears more than once in the any of the remaining denominators, then you must write down each additional occurrence as part of the LCD.
Step 3: Do any simple multiplication and write the final LCD.

Example 1 – Find the LCD of Example 1

Step 1: Factor each denominator into prime factors.
Step 1
Step 2: Write the first denominator down. Then look at each additional denominator and write down any new factors that were not in the first denominator. In this case, the x – 1 is new, but the x – 8 is not.
Step 2
Step 3: Do any simple multiplication and write the final LCD. In this case, no additional multiplication is needed.
Step 3

Example 2 – Find the LCD of Example 2

Step 1: Factor each denominator into prime factors.
Step 1
Step 2: Write the first denominator down. Then look at each additional denominator and write down any new factors that were not in the first denominator. In this case, the (x + 5) is new, whereas the 2 and x occur more than once in the second denominator so they must be listed again as part of the LCD.
Step 2
Step 3: Do any simple multiplication and write the final LCD.
Step 3

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Example 3 – Find the LCD of Example 3

Step 1: Factor each denominator into prime factors.
Step 1
Step 2: Write the first denominator down. Then look at each additional denominator and write down any new factors that were not in the first denominator. In this case, the (x + 4) occurs more than once in the second denominator it they must be listed again as part of the LCD.
Step 2
Step 3: Do any simple multiplication and write the final LCD. In this case, no additional multiplication is needed, but you can write (x + 4)(x + 4) as (x + 4)2.
Step 3

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Example 4 – Find the LCD of Example 4

Step 1: Factor each denominator into prime factors.
Step 1
Step 2: Write the first denominator down. Then look at each additional denominator and write down any new factors that were not in the first denominator. In this case, the (3x + 2) is a new factor in the second denominator and there are no new factors in the third denominator.
Step 2
Step 3: Do any simple multiplication and write the final LCD. In this case, no additional multiplication is needed.
Step 3

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Example 5 – Find the LCD of Example 5

Step 1: Factor each denominator into prime factors.
Step 1
Step 2: Write the first denominator down. Then look at each additional denominator and write down any new factors that were not in the first denominator. In this case, the –1 could be considered a new factor in which case the LCD would be –1(x – 3) or you could move the –1 to the numerator and the LCD would be (x – 3).
Step 2
Step 3: Do any simple multiplication and write the final LCD. In this case, no additional multiplication is needed.
Step 3

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