How the Least Common Denominator Calculator Works

Input Fractions:
The user can input fractions or whole numbers separated by commas in the text box. For example: 2 3/4, 5/8, 6/12, 4  Convert Mixed Numbers to Improper Fractions:
If the input includes mixed numbers (e.g., 2 3/4), the calculator will convert them to improper fractions. For instance: 2 3/4 becomes 11/4. 
Extract Denominators:
The calculator extracts the denominators from each fraction. Whole numbers are assumed to have a denominator of 1. For example: 11/4 → denominator = 4
 5/8 → denominator = 8
 6/12 → denominator = 12
 4 (whole number) → denominator = 1

Find the Least Common Denominator (LCD):
The calculator then finds the Least Common Denominator (LCD) by calculating the Least Common Multiple (LCM) of all the denominators. The LCM is the smallest number that each of the denominators divides into evenly.Formula:
$\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}$where GCD is the greatest common divisor.
To find the LCM of two numbers $a$ and $b$:In this case, the LCM of 4, 8, 12, and 1 is 24, so the LCD is 24.

Convert Fractions to Have the LCD:
Each fraction is then rewritten to have the LCD as its denominator. The calculator multiplies both the numerator and denominator of each fraction by the same factor to make the denominator equal to the LCD.Example Calculation:
$$\frac{11}{4}\times \frac{6}{6}=\frac{66}{24}$$
For $\frac{11}{4}$:Similarly:
$$\frac{5}{8}\times \frac{3}{3}=\frac{15}{24},\phantom{\rule{1em}{0ex}}\frac{6}{12}\times \frac{2}{2}=\frac{12}{24},\phantom{\rule{1em}{0ex}}\frac{4}{1}\times \frac{24}{24}=\frac{96}{24}$$  Results:
The calculator will display the LCD and the equivalent fractions with the LCD as the denominator. For the input: 2 3/4, 5/8, 6/12, 4
The results will be:

 2 3/4 → 66/24
 5/8 → 15/24
 6/12 → 12/24
 4 → 96/24
Example:
Input: 2 3/4, 5/8, 6/12, 4
Output:
 LCD: 24
 Equivalent Fractions: $$2\frac{3}{4}=\frac{66}{24},\phantom{\rule{1em}{0ex}}\frac{5}{8}=\frac{15}{24},\phantom{\rule{1em}{0ex}}\frac{6}{12}=\frac{12}{24},\phantom{\rule{1em}{0ex}}4=\frac{96}{24}$$