LCD Calculator

LCD calculator 

Find the LCD of any number of fractions through this calculator. This least common denominator (LCD) calculator gives a complete guide of the calculation process step-by-step.  

What is LCD?

LCD stands for the Least common denominator. It is basically the LCM, the least common multiple, of the denominators of the fractions. 

LCD is used when the fractions are to be added, subtracted, or multiplied. 

LCD formula:

The formula for the calculation of the least common denominator is:

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

This formula is applicable to two fractions only. 

How to find LCD?

Besides using the LCD calculator, there are three main methods to find the LCD. 

1. The formula method, using GCF.
2. The long division method
3. List of multiples

Let’s see separate examples for the first and the third method. 

Note: The long division method is explained in the respective calculator. Just enter the denominators in the calculator.

List of multiples:

The denominators are separated and their multiplied are listed. The first common multiple is the LCD.

Example:

For the following fractions, find the LCD.

2/3, 4/5, 5/6

Solution:

Step 1: Separate the denominators.

(3,5,6)

Step 2: List their multiples.

Multiples of 3:  6 9 12 15 18 21 24 27 30 33 36
Multiples of 5:  5 10 15 20 25 30 35 40 
Multiples of 6:  6 12 18 24 30 36 42

LCD = 30

Step 3: Make the equivalent fractions.

Multiply the fractions with such a number that the denominators become 30.

2/3 = ? / 30
2/3 x 10/10 = 20/30

4/5 = ? / 30
4/5 x 6/6 = 24/30

5/6 = ? / 30
5/6 x 5/5 = 25/30

The formula method:

Find the GCF of two fractions and put it in the formula. If there are three fractions, then make a pair of the first two. After solving, use the new fraction to complete the pair of the third fraction.

Example:

Find the LCD of the previous fractions using the GCF method.

2/3, 4/5, 5/6

Solution:  

Step 1: Separate the denominators.

(3,5,6)

Step 2: Find the GCF of denominators of the first two fractions. 

GCF of 3 and 5 is 1.

Step 3: Use the formula.

LCD = |a*b| / GCF (a,b)
LCD = |3*5| / GCF (3,5)
        = 15 / 1
        = 15

Step 4: Find the GCF of 15 and 6(the third denominator).

GCF of 15 and 6 is 3.

Step 5: Use the formula.

LCD = |a*b| / GCF (a,b)
LCD = |15*6| / GCF (15,6)
        = 90 / 3
        = 30

LCD of 3,5, and 6 is 30. Make the equivalent fractions using the previous method.