## Example Questions

### Example Question #1 : How To Find The Lowest / Least Common Denominator

What is the least common denominator of and ?      Explanation:

To find the least common denominator of two numbers, it is easiest first to factor them into prime factors:  Now, you need to compare each number and choose the case in which the prime factor has the highest power.  Therefore, since and are found only in , you will select those.  You can take "either" .  Finally, the in is the largest factor of .  Your LCD is found by multiplying all of these together: ### Example Question #2 : How To Find The Lowest / Least Common Denominator

Simplify:       Explanation:

To begin to solve this, you need to find the least common denominator of and .  The easiest way to do this is to begin by factoring them into prime factors:  The LCD is found by selecting the largest power for each factor across the two values.  Therefore, you will take , , and from and the from the .  Your LCD is therefore: .

Now, apply this to your fractions: ### Example Question #3 : How To Find The Lowest / Least Common Denominator

In simplest form,      Explanation:

First, find the smallest number that both and will factor into, which is .

This means that the fist fraction should be multiplied by and the second should be multiplied by .

Therefore, .

Then, add the numerators while the denomenators stay the same: .

Then, reduce the fraction to its lowest terms: .

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