Fraction form
Simple fraction
Values (enter up to 5 fractions)
1st fraction
Numerator (n₁)
Denominator (d₁)
2nd fraction
Numerator (n₂)
Denominator (d₂)
Least Common Denominator
Step by step solution?
No

# LCD Calculator - Least Common Denominator

By Hanna Pamuła, PhD candidate

Welcome to the LCD calculator - an intuitive tool that helps you find the least common denominator. All you need to do is input up to five fractions and we'll calculate the LCD and equivalent fractions with that denominator. Pretty straightforward, huh? 😉

However, if you'd like to first learn what the least common denominator is or how to find the least common denominator by hand ✍️ - we're here for you too. Scroll down and read our short & informative article about the lowest common denominator!

## What is the least common denominator? LCD in math

The least common denominator, also known as the lowest common denominator, is the lowest common multiple of the denominators of a given set. Usually we search for the least common denominator when we want to perform an operation on fractions, like adding fractions (and subtracting) or comparing fractions. For example:

• The LCD of 1/2 and 1/3 is 6, because LCM(2, 3) = 6;
• Knowing the LCD, you can find equivalent fractions to yours 1/2 and 1/3, with the denominator equal to found LCD:

1/2 = 3/6

1/3 = 2/6.

• Now it's easy to add the fractions, subtract them or compare:
• 3/6 + 2/6 = 5/6
• 3/6 - 2/6 = 1/6
• 3/6 > 2/6

However, if you've just googled the question "What is a LCD?", and you looked for the least common denominator definition, the search results may be a bit surprising to you 😮. The abbreviation LCD also stands for a Liquid Crystal Display - a type of display we have in our computers 💻, TV screens 📺, digital cameras 📽️, watches ⌚ and smartphones 📱. So next time, try "What is a LCD in math?" instead 😉

## How to find the least common denominator?

Well, the easiest and most straightforward method is to use our LCD calculator - that's why you are here, right? 😉

Jokes aside - we really appreciate that you'd like to learn how to find the least common denominator. There are a couple of methods, and we'll describe four of them here. So let's present them with a relatively simple example:

Assume that we have three fractions: `1/2`, `3/8`, and `11/12`. What's the LCD value? What are the equivalent fractions, with the same denominator?

First, we need to find the lowest common denominator of our fractions. Read about the four methods below and choose the way you like the most.

## Method 1. The list of multiples

Listing multiples is a brute force method. It may be useful in special cases, e.g., if the numbers are relatively small. So, how to find the least common denominator? Make a list of the multiples of each number, until you find the first common multiple of all the numbers:

• Multiples of 2:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28...

• Multiples of 12:

12, 24, 36, 48, 60 ...

• Multiples of 8:

8, 16, 24, 32, 40, 48 ...

It's usually not a recommended method, imagine listing the common denominators of 2 and 1000 - it doesn't make much sense, does it? :)

## Method 2. Using prime factorization

Another method to find out the lowest common denominator is the prime factorization method:

#1 Write down all of the numbers as a product of their prime factors:

• Prime factorization of 2:

`2 = 2¹`

• Prime factorization of 12:

`2 * 2 * 3 = 2² * 3¹`

• Prime factorization of 8:

`2 * 2 * 2 = 2³`

#2 Find highest power of each prime number:

`2³`, `3¹`

#3 Multiply these values together:

`2³ * 3¹ = 24`

## Method 3. Using the greatest common divisor (factor)

You can calculate the LCD from the Greatest Common Factor (GCF) value:

`LCD(a,b) = |a * b| / GCF(a,b)`

where `|a * b|` is the absolute value of `a * b`.

#1 Substitute the first two numbers (2 and 8) into the formula:

`LCD(2, 8) = |2 * 8| / GCF(2, 8)`

we know that `GCF(2, 8) = 2` so:

`LCD(2, 8) = 16 / 2 = 8`

#2 Find the LCD of the result from the previous step (i.e., 8) and the next number in the list, 12:

`LCD(12, 8) = |12 * 8| / GCF(12, 8)`

we calculate that `GCF(12, 8) = 4` so:

`LCD(12, 8) = 96 / 4 = 24`

The last method is the ladder method. Many students like this technique, so check it out and maybe you'll have a new favorite:

#1 Start by writing all of your numbers next to each other:

 2 8 12

#2 Find a prime number that can divide at least two of your numbers (without remainder). Write that prime number on the left hand side:

 2 2 8 12

#3 Divide your original numbers by the prime and write the quotients under the original numbers. If your number is not evenly divisible, simply write that number in again:

 2 2 8 12 1 4 6

#4 Repeat until the whole table is complete:

 2 2 8 12 2 1 4 6 2 1 2 3 1 1 3

#5 Find the LCD by multiplying all the values in the orange "L" around your table/cake:

`2 * 2 * 2 * 1 * 1 * 3 = 24`

Check out our LCM calculator, where the calculator shows how to find the least common denominator - A.K.A. the least common multiple. Because, all in all, finding the LCM and LCD are pretty much the same thing!

## Least common denominator in practice

Now that you know the LCD value, you can come to the second step - finding the fractions that are equivalent to your basic fractions, but with the same denominator - 24 in our case:

• `1/2 = ?/24`, to get the 24 as the denominator, multiply the fraction by 12/12 (because 24 / 2 = 12):

`1/2 = 1/2 ⋅ 12/12 = 12/24`

• `3/8 = ?/24`, multiply by 3/3 to get 24 as a bottom number:

`3/8 = 3/8 ⋅ 3/3 = 9/24`

• `11/12 = ?/24`, as 24 / 12 = 2, multiply the fraction by 2/2:

`11/12 = 11/12 ⋅ 2/2 = 22/24`

And that's it! After the reading, you've (hopefully) understood what the least common denominator is and learned about four methods that can help you find the LCM in math. So, what now? It's time to check how the LCD calculator works!

## How to use the LCD calculator?

Check out this step-by-step guide if you have any doubts on how to use our tool:

1. Choose the type of fraction. If you're into simple fractions, leave it as it is. If at least one of your number is a mixed number (or a whole number), pick the "mixed number" option.
2. Enter the fractions. Let's say we want to find the LCD of the fractions 1/4 and 11/14. For the first fraction, input 1 as the numerator and 4 as the denominator; for the second one, the numerator is 11 and denominator equals 14.
3. Calm down, relax, and read the result - this LCD calculator did the job and found the lowest common denominator! It's 28.

Additionally, the tool displays the equivalent fractions with the LCD value as the denominator:

• 1/4 = 7/28; and
• 11/14 = 22/28.
1. If you like, you can even choose the option "step-by-step solution". You'll learn some details on how to find the LCD in math from it!

## Real-life applications of the lowest common denominator

Now that you know what the least common denominator is - and how to find it - let's talk about some LCD applications. We can almost hear you moaning "But where will I ever use it?" No worries - the lowest common denominator is helpful in many life situations. You can use it any time you want to "align" two or more things of different lengths, e.g.:

• In construction 🏗️, e.g. when building a wall from bricks or working with tiles of different lengths;
• In music 🎵 - when computing the smallest number of beats for the combined rhythm; and
• When organizing work schedules 📅 - e.g., in the situation that one employee has a day off every 6 days, and the other every 4 days, you can calculate when both of them are absent.
Hanna Pamuła, PhD candidate