How to find the lowest / least common denominator

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GRE Quantitative Reasoning › How to find the lowest / least common denominator

Questions 1 - 3
1

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:

2

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:

.

3

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:

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