The least common denomiator (or least common multiple...same concept) is the least expression that both denominators can go into. I like to work step by step with each term. Let's start with the numerical coefficients.

The least common multiple of 12 and 60 is 60. You can figure this out by writing out multiples of 12 and 60 and seeing the first one they have in common.

Now let's move on to the a's.

There's an and an Therefore, their LCM is .

Do the same with the b's and the c's; and , respectively.

Now put those all together to get .

To simplify this problem we need to find the least common denominator between the two fractions. To do this we look at 5 and at 8. The least common number between these two is 40.

In order to rewrite each fraction in terms of a denominator of 40 we need to muliple as follows:

we are able to mulitply by 8/8 and 5/5 because those fractions are really just 1 written in a different format.

Now using order of opperations we get the following

Now we have a common denominator and can do our addition to get the simplfied number:

The least common denominator is the lowest number that is divisible by all the denominators in the expression. Write out some of the factors of each denominator.

Notice that each factor shares twenty as the common denominator and can be converted to this denominator to solve.

The answer is:

When finding the least common denominator, the quickest way is to multiply the expression out. In this case and don't share any factors other than . We can multiply this to get as the final answer.

Remember when foiling, you multiply the numbers/variables that first appear in each binomial, followed by multiplying the outer most numbers/variables, then multiplying the inner most numbers/variables and finally multiplying the last numbers/variables.

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:

When finding the least common denominator, the quickest way is to multiply the expression out. In this case and share a factor other than which is . If you don't see that. just break down the quadratic equation to simple factors. Remember, we need to find two terms that are factors of the c term that add up to the b term.

The quadratic becomes . By factoring out , we get and . Just multiply the leftovers and the factored expression to get .

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:

In order to be able to find , we must first find the least common denominator. In this case, it is :

The equation can now be written as:

Solving for , we get:

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:

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: