LCD Calculator

Least Common Denominator Calculator

LCD calculator finds the least common denominator of fractions, non-fraction, and mixed numbers quickly, with detailed steps. This LCD finder makes calculation easy by calculating the LCM of the denominators of all fractions. 

What is the Least Common Denominator (LCD)?

The Least Common Denominator (LCD) is the smallest number that helps to make the common denominator of group fractions/nonfraction numbers. It is a positive integer that is divisible by each denominator of given fractions.

The LCD is also known as the lowest common denominator or smallest common denominator of the group of fractions. It can be determined by finding the LCM of the denominators of the fractions. 

The LCD calculation is used for addition or subtraction of fractions and arranging the fractions from the least to greatest order. 

Methods to find LCD?

There are four different manual methods used to find the Lowest common denominator (LCD) of a group of fraction or non-fraction numbers. The easiest way is to use our lcd calculator. 

The names of these methods are:

• List of Multiples/Factors
• Prime Factorization
• Division Method
• Greatest Common Divisor (GCD) Method

Below we discuss the details of some methods to understand LCD calculation. Also, perform their examples with detailed explanations. 

How to Find LCD?

As discussed above different methods to find the LCD of integers, mixed numbers, or mixed fractions but first convert all fractions into simple fraction numbers. 

Then calculate the LCD of all denominators by finding the LCM of the denominator using any method of LCD. To find LCM of any number use LCM Calculator. 

To evaluate the LCD of any set of numbers (fraction, mixed fraction, and integers) follow the below steps:  

• First, Convert each integer or mixed fraction number into a simple fraction.
• Then find the LCD of the denominators of all fractions by following the LCD methods (Prime Factorization, List of Multiples, or Division method) or finding the least common multiple.
• Finally, convert inputs to equivalent fractions by multiplying and dividing the LCD with each fraction. 
• After simplification make the denominators the same according to LCD and get the final fractions.

For a better understanding, see the example below, which uses different methods.

• Find LCD Using List of Multiples

The smallest common denominator finding by a list of multiple is the easiest method. First, make a List of the few multiples of each denominator. 

Then find the smallest common multiple that appears in all lists of numbers. This smallest number is the required LCD of the given fractions. To make a list of multiple numbers, use Multiples calculator.

Example

If the fractions {4/3, 7/5} and denominators are 3 & 5, find its LCD with a list of multiple and the equivalent fraction with LCD.

Solution:

The given fractions are already in the fractions form then the first step can skip out.

Step 1: Now, find the list of multiple for the denominator values. 

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33...
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50...

Step 2: Note the smallest number.

In this case, the LCD of given numbers is “15”. 

The equivalent fraction according to the LCD, by multiplying or dividing the LCD value with each fraction becomes:

4/3 = 4/3 × 15/15 = 20/15

7/5 = 7/5 × 15/15 = 21/15

Alternatively, use our common denominator calculator to calculate the LCD effortlessly.

• Find the LCD Using Prime Factorization

The least common denominator calculation by the use of prime factorization is one important method from all methods of LCD. In this method, find the prime factor of the denominator of all fractions. 

Then note the common & uncommon factors from all prime factors and multiply all of them to find the lowest common denominator. But a common factor takes one time from all of them. To evaluate the prime factors of any number use prime factorization calculator. 

For more understanding see the below example, in which find LCD with prime factorization.

Example: Find the LCD of {7/12, 4/15} by prime factorization. For the verification of results use lowest common denominator calculator.

Solution

Step 1: First, find the prime factor of the denominator by factorization.

12 = 2 x 2 x 3 = 22 x 3

15 = 3 x 5 

Step 2: Note the common & uncommon factors and multiply all of them.

Common Factor= 3,               Uncommon Factor = 22 x 5

LCD (12, 15) = 22 x 3 x 5 = 4 x 3 x 5 = 60

LCD (12, 15) = 60

Step 3: Now, convert the given fraction into equivalent fractions with LCD, by multiplying or dividing LCD value with each fraction.

7/12 = 7/12 × 60/60 = 35/60

4/15 = 4/15 × 60/60 = 16/60

Thus, the LCD is 60, and the equivalent fraction with LCD as a denominator is 35/60 & 16/60 by prime factorization. 

• Finding LCD Using GCD Method

To find the LCD with GCD method is one new way that uses the LCD formula. In this method firstly find the GCF of all denominators. Then multiply the all denominator’s values with each other and divide the product by the GCD/GCF that is found in the starting. 

To find the GCF values use our GCF calculator. The mathematical formula, used in this method to find LCD is stated as: 

LCD Formula = Product of the numbers/GCD of the numbers

Example: 

Find the LCD of {7/15, 5/6} using the GCD method and convert it into the equivalent fractions with LCD. 

Solution:

Step 1: First find the GCD of all denominators. 

To find GCD, find the factors of all denominators and note the highest common factors.

Factors of 15 = 1, 3, 5, 15

Factors of 6 = 1, 2, 3, 6

Note that, the highest common factor is 3.

So, GCD of 15 and 6 is 3.

Step 2: Now, multiply all denominator’s values.

Product of denominators = 15 × 6 = 90

Step 3: Put the values in LCD formula and simplify to evaluate the LCD. 

LCD Formula = Product of the numbers/GCD of the numbers

           = 90/3 = 30

Thus, the LCD is 30.

Now, convert the given fraction into equivalent fractions with LCD.

7/15 = 7/15 × 30/30 = 14/30

  5/6 = 5/6 × 30/30 = 25/30