LCD Calculator- Least Common Denominator

With our LCD Calculator- Least Common Denominator, you can find the lowest common denominator, starting with two up to five fractions. Thus, an intuitive calculator helps you find the least common denominator fractions in math. Take a look our golden ratio.

All you need is to add up to five fractions to our LCD calculator. So, we will evaluate the LCD and equivalent fractions with these denominators. But, if you don’t know what the least common denominator is or wonder how to find the least common denominator, we will help you.

Furthermore, scroll down for more in-depth information about this subject. So, let’s dive into this.

Least Common Denominator (LCD) – Definition

In the first place, let’s define the least common denominator in math. LCD is the lowest common of multiple denominators with a set of fractions. Further, it is also known as the lowest common denominator. Therefore, you can utilize it to create a set of equivalent fractions (and subtracting) so that all have the same denominator.

Now, let’s apply some numbers to explain what we learned. For example, the LCD of 1/2 and 1/3 is 6. Because of that, LCM for 2 and 3 is 6. So then, when you know the LCD, you can now find equivalent fractions for 1/2 and 1/3 with the divisor equal to find LCD.

To summarize: 1/2 = 3/6 and 1/3 = 2/6. After this, it’s easy to set up the fractions, subtract and compare them. Also, these relations can be written:

• 3/6 + 2/6 = 5/6,
• 3/6 – 2/6 = 1/6,
• 2/6 < 3/6.

How to Find the Least Common Denominator: Methods

Indeed, there are a couple of methods that you can operate to find the least common denominator. We will define four of them. So let’s introduce them with a proportional example below. Furthermore, we have three fractions. So it is 1/2, 3/8, and 11/12. Thus, we need to find the least common denominator value.

Further, what are the equivalent fractions but with the same denominator? So firstly, we need to find the lowest common denominator of our fractions to do that. In the meantime, read about the methods and choose what you like the most.

LCD Methods

• The list of multiples

Listing multiple may be useful if the numbers are relatively small. Then how to find the least common denominators? First, multiple create the list of each number. Next, you need to make the first common multiple of all the numbers.

Let’s utilize multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …
Now, we’ll operate multiples of 12: 12, 24, 36, 48, etc. This method isn’t recommended because of its long listing.

• Using prime factorization

With this prime factorization method, you need to write all the numbers as a product of their prime factors. After, you need to find the highest power of each prime number. Then, to conclude, multiply these values together.

• Using the greatest common divisor

This method allows you to calculate the LCD from the greatest common divisor (factor) – GCF. To apply this, substitute the first two numbers into the formula below: 

LCD(a, b) = \frac {a \times b} {GCF (a\times b)}

• Drawing table/grid/ladder/cake

So, this is the last method. You’ll like this technique if you’re studying mathematics. It’s easy and fun. Firstly, write all numbers next to each other. Secondly, find a prime number that can divide at least two of your numbers.
Then, write it on the left-hand side. After that, divide the original numbers by the prime. Also, write the quotients under the original numbers. Repeat it till the whole table is complete. And in the end, find the LCD by multiplying all the values in the orange L around the table/cake.

LCD Calculator: How to Use?

Our LCD calculator is easy to work with, especially if you haven’t utilized it before. And you don’t need to be brilliant in mathematics. Furthermore, check our step-by-step guide to help you with our calculator. To begin with, you need to choose the type of fraction. But, if your fractions are simple, go away to the next step. 

Eventually, if at least one of your numbers is mixed, then pick the ‘mixed number‘ option below. Then, add the fractions. To explain, we’ll find the LCD of fractions 3 and 6. For the first fraction, put on the number 3 as the numerator. Then leave the denominator empty. Now, click on the plus to put the second fraction. In that box, write 6 as the second numerator.

The result will come out quickly. Under those circumstances, our LCD calculator did the job, and the LCD is 6.

LCD Calculator – Example

To demonstrate, we’ll work on two examples to make it clear and easy. So let’s go step by step. Firstly, we’ll go with the easier one. Let’s find the least common denominator of 1/2 and 5/6. To begin, first, open our LCD calculator. You can use it neither on desktop nor mobile.

First example:

1. Firstly, choose the simple fraction. Next, go to the first fraction form, where you’ll see two boxes. In the numeration box, put in number 1. Then put number 2 in the denominator box below.
2. After that, go to the plus under this, and make one more fraction. And do the same with the 5/6 like in the previous one. Number 5 is input in the numerator, and 6 goes into the denominator box.
3. You will see the results quickly. The least common denominator is 6.

Second example: we choose the mixed number to demonstrate the calculation. Example, 1 1/2, 2/4, 3/6, and 2 3/8 to find LCD.

1. Again, open our calculator use the mixed form number. Put on the whole number. In this case, it’s 1.
2. Then enter 1 and 2 in the numerator and denominator boxes as we explain in the first example.

• W- whole number
• n- numerator and
• d- denominators.

After you enter all four fractions, you’ll see results. It’s 24 LCD.

Least Common Denomination: Real-world Usage

To summarize, you know what the least common denominator is and how to find it. Now, it’s time to learn where you can use it. Surprisingly, the it is helpful in many life situations. In short, you can use it in construction, music, and organizing your work schedule.

To sum up, our calculator is super handy when you’re building a wall from bricks. Or perhaps while working with tiles of different lengths.

Furthermore, let’s imagine this situation. One of your employees has a day off every five days. Another one has every four days. In that case, you can calculate when both of them are absent using our LCD calculator.

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