Least Common Denominator
Master calculations with mixed numbers and fractions.
Calculate the LCD of any set of fractions with this least common denominator calculator by CalcoPolis. This convenient tool will allow you to order, add, and subtract fractions much faster.
Additionally, you can use this quick guide to review the definition, applications, and solving methods of the LCD. Let's get started!
What Is the Least Common Denominator?
The Least Common Denominator (LCD) is the smallest number the common denominator for your given set of fractions can be.
The fractions 5/15 and 10/20 can be renamed into 20/60 and 30/60.
The number 60 is the lowest denominator, that's common for both of the fractions.
Thus, 60 is the LCD.
To get the LCD, you'll need to know the Least Common Multiple (LCM) of the denominators of two or more fractions. The LCM is the smallest multiple that two or more numbers have in common.
We can find the LCM of 15 and 20 by listing the multiples of both numbers until we find their smallest common multiple.
The multiples of 15 are 15, 30, 45, 60, 75, and so on.
The multiples of 20 are 20, 40, 60, 80, 100, and so on.
As you can see from the list, the least common multiple is 60.
How Does the LCD Help in Calculations?
The least common denominator is quite handy when dealing with fractions and their operations.
You can use your knowledge of the LCD to arrange fractions in ascending or descending order.
To arrange 5/12, 7/8, and 9/16 in ascending order, we need to know their least common denominator first.
Once we figure out that the LCD is 48, we can now rename the fractions as follows:
5/12 = 20/48
7/8 = 42/48
9/16 = 27/48
After renaming the fractions using their LCD, it's now easier to spot the smallest and biggest fractions.
Ascending order: 5/12, 9/16, 7/8
Adding and Subtracting Fractions
Similarly, being familiar with LCDs can help you quickly add and subtract fractions.
To add 2/15, 1/5, and 4/10 together, let's use 30, their LCD, to rename them as follows:
2/15 = 4/30
1/5 = 6/30
4/10 = 12/30
Then, we can proceed in adding all three fractions easily.
4/30 + 6/30 + 12/30 = 22/30
How to Calculate the Least Common Denominator?
You can solve for the LCD using the following methods:
The simplest way to find the LCD is to take the denominators of your fractions and list down their multiples. The first and least multiple that they have in common is the LCD.
To find the LCD of 1/4 and 3/6, let's list down their multiples.
The multiples of 4 are 4, 8, 12, 16, 20, and so on.
The multiples of 6 are 6, 12, 18, 24, 30, and so on.
Based on the list, the least common denominator is 12.
The renamed fractions will be 3/12 and 6/12.
Using the Greatest Common Factor (GCF)
Another way to get the LCD is to use the GCF of the denominators. All you have to do is multiply the denominators, and divide their product by the GCF.
To find the LCD of 3/9 and 5/12, we'll use the GCF of the denominators, which is 3.
First, let's multiply the denominators.
9 x 12 =108
Next, let's divide the product by the GCF.
108 divided by 3 is 36.
Therefore, 36 is the LCD.
The renamed fractions will be 12/36 and 15/36.
Hopefully, this least common denominator calculator has helped you understand and calculate your LCDs in a flash. Don't forget to keep visiting CalcoPolis for access to over a hundred business tools and math calculators.
Even though the described examples seem pretty straightforward, it is easy to make a mistake. That's why it is good practice to use our calculator regularly to avoid calculus mistakes.