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LCD Calculator

LCD Calculator

Write down the fractions separated by commas in the designated box and the calculator will find their LCD (least common denominator), with detailed calculations shown.

Enter Numbers or Fractions: (separated by commas)

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Let this free LCD calculator find the least common denominator of each and every kind of fractions combination. The most important purpose of this lowest common denominator calculator is to create ease for you while you perform arithmetic operations on LCD fractions.

Well enough! Let’s revise the concept of the lowest common denominator in brief detail.

What Is Least Common Denominator?

“The smallest number that can be considered as the common denominator for a couple of fractions or more is called LCD.”

Basically, the common denominator is actually the multiple of each fraction’s denominator in a set. The free LCD calculator looks for this common number and displays it on your screen in seconds.

How To Find LCD of Integers, Fractions, or Mixed Numbers?

The least denominator is the second name used for the least common multiple that you can find using various methods.

Moreover, we will be discussing the summary of all methods in a couple of steps below:

  • First of all, you need to convert all integer numbers and mixed numbers into improper fractions
  • After this, determine the lowest common denominator of all fractions
  • In the end, write all the resulting fractions by using LCD as denominator all

The free LCD calculator also follows all the above-mentioned terms and conditions to find the common denominator.

LCD Table:

Here we have a table that goes for showing the smallest common denominators for various fraction combinations:

Fractions

LCD
1/2, 1/4

4

1/2, 1/3

6
2/3, 5/9

9

2/3, 4/9, 5/6

18
2/3, 3/4, 4/5

60

2/3, 4/5

15
2/3, 1

3

2/3, 3/5, 4/7

105
2/3, 2

3

2/3, 6/7

21
3/4, 6/7, 9/8

56

3/2, 5/4

4

3/4, 1/2

4

3/4, 5/6

12
3/6, 2/12

12

4/5, 2/3, 5/7

105
4/5, 5/6, 7/15

30

4/3, 8/9, 3/5

45
5/6, 15/8

24

5/2, 8/9, 11/14

126
5/9, 4/15, 1/45

45

6/5, 8/25

25
6/8, 4/32

32

8/9, 10/27, 16/81

81
8/51, 19/85

255

9/2, 3, 9/4

4
9/14, 3/7

14

You can pick any fraction set from the above table and validate the results by the assistance of our free to use LCD calculator.

How To Find The Least Common Denominator Numerically?

What do you think about resolving a couple of examples to recall your concept? Let’s do it together!

Example # 01:
How to find the LCD for the following set of fractions:
3, 1 2/3, 4/5, 5/8

Solution:

Here we have:

3 = 3/1

1 2/3 = 5/3

Now we will take all the denominators and find their LCD as follows:
1, 3, 5, 8

LCD = 120

Equivalent fractions with LCD:

3 = 3 * 120/120 = 360/120

1 2/3 = 1 2/3 * 40/40 = 200/120

4/5 = 4/5 *24/24 = 96/120

5/8 = 5/8 * 15/15 = 75/120

So we have:

Equivalent Fractions = 360/120, 200/120, 96/120, 75/120

You can also commence this free to use least common denominator calculator to verify the authenticity of results. 

Example # 02:
You are given the following combination of fractions:

3/5, 6/3, 6/2, 3/9, 4

How to find least common denominator for this LCD fractions combination.

Solution:
Here:

4 = 4/1

Here we have the denominators as follows:

5, 3, 2, 9, 1

Fraction common denominator = 90

Equivalent fractions with LCD:

3/5 = 3/5 * 18/18 = 54/90

6/3 = 6/3 * 30/30 = 180/90

6/2 = 6/2 * 45/45 = 270/90

3/9 = 3/9 * 10/10 = 30/90

4 = 4/1 * 90/90 = 360/90

So we have:

Equivalent Fractions = 54/90, 180/90, 270/90, 30/90, 360/90

How LCD Calculator Works?

This least common denominator calculator takes into consideration integers, fractions, or mixed numbers to determine the smallest common positive integer number. Let’s have a look at its operation!

Input:

  • Write down numbers, mixed numbers, or fractions in the designated box
  • Make sure that you separate all numbers or fractions by commas
  • After you are done, tap the calculate button

Output:

The free common denominator finder finds:

  • The lowest common denominator of the fractions set that is provided
  • Equivalent fractions with the same LCD

FAQ’s:

What is the least common denominator for 3/8, 9/2, and 8/5?

The smallest common denominator for given fractions is 40 that you could also cross check by using an LCD calculator.

What is the common denominator for the fractions given below:
-2/7, 9/9, -4 7/3

The LCD for the given fraction combination is 63.

Is there any difference between LCM and LCD?

Yes, of course! You can consider LCD as the special case of LCM. The LCD is the LCM but it is true for the denominators of the fractions.

What do you mean by common numerator?

A particular number that is actually the multiple of all the numerators of fractions involved in a set is called their common numerator.

How would you compare fractions with unlike denominators?

If we have the fractions with unlike denominators, then the only way to compare them is figuring out their LCD. Moreover, the fastest method to compare them is using an online least common denominator calculator.

Whats a common denominator for the fractions 9/7 and 2/7?

As these are fractions with common denominators, so their LCD will also be 7.

How to recognize the smaller or larger fraction with the same numerators?

Let’s suppose that you have a couple of fractions that have the same numerators, always remember that the fraction with the bigger denominator is considered the smaller one. On the other hand, the fraction with the smaller denominator is the one that is bigger.

What type of fractions have different denominators?

The fractions having different denominators are said to be unlike fractions.

What is the smallest positive fraction in the world?

10/60 is the smallest fraction in the world. This is because 10/60 = 1/6 = 0.16666…

Conclusion:

The main focus of determining the LCD is to simplify the addition, subtraction, multiplication, and division of fractions. This is why our best LCD calculator is the most fast and reliable way of finding the lowest common denominator of fractions set. It will help you resolve fraction problems more authentically.

References:

From the source of Wikipedia:, Description, Role in arithmetic and algebra, Practical uses

From the source of Khan Academy: Least common multiple, repeating factors

From the source of Lumen Learning: Listing Multiples Method, Prime Factors Method