### All GRE Math Resources

## 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:**

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:**

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:**

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:

.