GRE Math : How to find the lowest / least common denominator

Study concepts, example questions & explanations for GRE Math

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Example Questions

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

What is the least common denominator of  and ?

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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,  

Possible Answers:

Correct answer:

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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