In order to find the least common denominator, write out the factors for both denominators.  The LCD is the smallest number divisible by both denominators.

Notice that they both share 99 as a common denominator.

The answer is:  

The least common denominator is the term that is divisible by both of the uncommon denominators.  

Notice that if we multiplied the  quantity by two, we will get the denominator of the second term and the second fraction can be left unchanged.

We do not need to use the FOIL method to determine the least common denominator.

Do not solve the expression.

The answer is:  

The least common denominator can be determined by writing the factors of each denominator provided.  

Notice that the least common denominator is the least number that is divisible by all the denominators of the fractions.  The common factors are 48 and 96.

The first number to appear is 48.

The answer is:  

The least common denominator is the minimal term that is divisible by all the denominators in the fractions.

Notice that the first two fractions has an x-term, and the ten does not have an x-term.  We will need to multiply an x-variable to the ten.

Now that all the denominators share an x-term, we will concentrate on the multiples of each denominator coefficient.

The coefficient must be .

This means that the least common denominator must be , since this is divisible by all the denominators in the expression.

The answer is:   

In order to find the least common denominator, we will need to determine the minimal value that is divisible by all three denominators.

Write out the multiples for every denominator.  Notice that 16 is the minimum that the number that should be started with.

All three denominators share 48 as a result.

The answer is:  

In order to determine the least common denominator, we will need to start with the largest denominator, write the multiples for that denominator, and visually determine whether if the multiples are divisible by the next highest denominator.

Stop at 160, since this is the first multiple that is divisible by both four and twenty.

The means that the least common denominator is 160.

The answer is:  

To simplify the sum of the two fractions, we must find the common denominator.

Simplifying the denominator of the first fraction, we get

because the denominator is a difference of two squares, which follows the form

Now, we can rewrite the sum as

It is far easier to see the common denominator now:

Find the least common denominator (LCD) and convert each fraction to the LCD and then add.  Simplify as necessary.

The result is an improper fraction because the numerator is larger than the denominator and can be simplified and converted to a mix numeral.

Since the denominator is the same in both expressions, we can perform the subtraction in the numerator. The result will have the same denominator of 6x³y.

Simplify the expression:

To solve, we must first find a common denominator between 3, 4, and 12. All 3 numbers are factors of 12 and therefore 12 can be the common denominator. Then the numerators must be multiplied by the same factor as the demominator was.

This gives us our new fractions: 

Next, we add the numerators, but our denominators stay the same: 

.

Lastly, we simplify to get  as our answer.