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# Least Common Denominator

... is the Least Common Multiple of the denominators ...

First, let's be clear what a Denominator is:

## Fractions

A Fraction (such as 3/4) has two numbers:
 Numerator Denominator
We call the top number the Numerator, it is the number of parts you have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

## Fractions with Different Denominators

Sometimes you have two (or more) fractions with different denominators - you may want to add or subtract them - but you need to make the denominators the same before you can do that:

### Example: What is 3/8 + 5/12 ?

Let's try to make the denominators the same ... if you multiply 8 × 3 you get 24, and if you multiply 12 × 2 you also get 24. So, let's try that (important: what you do to the bottom of the fraction, you must also do to the top):

 × 3 3 = 9 8 24 × 3
and,
 × 2 5 = 10 12 24 × 2

Now we can do the addition: 9/24 + 10/24 = 19/24.

## How to Make the Denominators the Same

The trick is to find the Least Common Multiple of the denominators. (Read about Least Common Multiples now, if you haven't already.)

In the previous example, the Least Common Multiple of 8 and 12 was 24. And so the the Least Common Denominator of 3/8 and 5/12 is 24

So, here are the steps: • Find the Least Common Multiple of the denominators (this is called the Least Common Denominator).
• Change each fraction (using equivalent fractions) to make their denominators the same as the least common denominator
• Then you can do whatever you want with the fractions (add, subtract, etc) !

### Example: What is 1/6 + 7/15 ?

The Least Common Multiple of 6 and 15 is 30 (try to work that one out yourself!). So, let's do some multiplying to make each denominator equal to 30:

 × 5 1 = 5 6 30 × 5
and,
 × 2 7 = 14 15 30 × 2

Now we can easily do the addition: 5/30 + 14/30 = 19/30.

## Least Common Multiple Tool

To find the least common denominator automatically, you can use our Least Common Multiple Tool - just put in the denominators, press the button, and the least common denominator is shown for you.