The **lowest Common Denominator** or **Least Common Denominator** is the Least Common Multiple of the denominators of a set of fractions.

**Common denominator** : when the denominators of two or more fractions are the same.

Least Common denominator is the smallest of all common denominators.

Why do we need **LCD** ?

It simplifies addition, subtraction and comparing fraction.

Common Denominator can be simply evaluated by multiplying the denominators. In this case, 3 * 6 = 18

But that may not always be least common denominator, as in this case LCD = 6 and not 18. LCD is actually LCM of denominators.**Examples : **

LCD for fractions 5/12 and 7/15 is 60. We can write both fractions as 25/60 and 28/60 so that they can be added and subtracted easily. LCD for fractions 1/3 and 4/7 is 21.

Example Problem : Given two fractions, find their sum using least common dominator.**Examples**:

Input : 1/6 + 7/15 Output : 19/30 Explanation : LCM of 6 and 15 is 30. So, 5/30 + 14/30 = 19/30 Input : 1/3 + 1/6 Output : 3/6 Explanation : LCM of 3 and 6 is 6. So, 2/6 + 1/6 = 3/6

**Note*** These answers can be further simplified by Anomalous cancellation.

## C++

`// C++ Program to determine` `// LCD of two fractions and` `// Perform addition on fractions` `#include <iostream>` `using` `namespace` `std;` `// function to calculate gcd` `// or hcf of two numbers.` `int` `gcd(` `int` `a, ` `int` `b)` `{` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `return` `gcd(b % a, a);` `}` `// function to calculate` `// lcm of two numbers.` `int` `lcm(` `int` `a, ` `int` `b)` `{` ` ` `return` `(a * b) / gcd(a, b);` `}` `void` `printSum(` `int` `num1, ` `int` `den1,` ` ` `int` `num2, ` `int` `den2)` `{` ` ` `// least common multiple` ` ` `// of denominators LCD` ` ` `// of 6 and 15 is 30.` ` ` `int` `lcd = lcm(den1, den2);` ` ` `// Computing the numerators for LCD:` ` ` `// Writing 1/6 as 5/30 and 7/15 as` ` ` `// 14/30` ` ` `num1 *= (lcd / den1);` ` ` `num2 *= (lcd / den2);` ` ` `// Our sum is going to be res_num/lcd` ` ` `int` `res_num = num1 + num2;` ` ` `cout << res_num << ` `"/"` `<< lcd;` `}` `// Driver Code` `int` `main()` `{` ` ` `// First fraction is 1/6` ` ` `int` `num1 = 1, den1 = 6;` ` ` `// Second fraction is 7/15` ` ` `int` `num2 = 7, den2 = 15;` ` ` `printSum(num1, den1, num2, den2);` ` ` `return` `0;` `}` |

## Java

`// Java Program to determine LCD of two` `// fractions and Perform addition on` `// fractions` `public` `class` `GFG {` ` ` ` ` `// function to calculate gcd or` ` ` `// hcf of two numbers.` ` ` `static` `int` `gcd(` `int` `a, ` `int` `b)` ` ` `{` ` ` `if` `(a == ` `0` `)` ` ` `return` `b;` ` ` ` ` `return` `gcd(b % a, a);` ` ` `}` ` ` ` ` `// function to calculate lcm of` ` ` `// two numbers.` ` ` `static` `int` `lcm(` `int` `a, ` `int` `b)` ` ` `{` ` ` `return` `(a * b) / gcd(a, b);` ` ` `}` ` ` ` ` `static` `void` `printSum(` `int` `num1, ` `int` `den1,` ` ` `int` `num2, ` `int` `den2)` ` ` `{` ` ` ` ` `// least common multiple of` ` ` `// denominators LCD of 6 and 15` ` ` `// is 30.` ` ` `int` `lcd = lcm(den1, den2);` ` ` ` ` `// Computing the numerators for LCD:` ` ` `// Writing 1/6 as 5/30 and 7/15 as` ` ` `// 14/30` ` ` `num1 *= (lcd / den1);` ` ` `num2 *= (lcd / den2);` ` ` ` ` `// Our sum is going to be res_num/lcd` ` ` `int` `res_num = num1 + num2;` ` ` ` ` `System.out.print( res_num + ` `"/"` `+ lcd);` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` ` ` `// First fraction is 1/6` ` ` `int` `num1 = ` `1` `, den1 = ` `6` `;` ` ` `// Second fraction is 7/15` ` ` `int` `num2 = ` `7` `, den2 = ` `15` `;` ` ` `printSum(num1, den1, num2, den2);` ` ` `}` `}` `// This code is contributed by Sam007.` |

## Python3

`# python Program to determine` `# LCD of two fractions and` `# Perform addition on fractions` `# function to calculate gcd` `# or hcf of two numbers.` `def` `gcd(a, b):` ` ` ` ` `if` `(a ` `=` `=` `0` `):` ` ` `return` `b` ` ` `return` `gcd(b ` `%` `a, a)` `# function to calculate` `# lcm of two numbers.` `def` `lcm(a, b):` ` ` ` ` `return` `(a ` `*` `b) ` `/` `gcd(a, b)` `def` `printSum(num1, den1,` ` ` `num2, den2):` ` ` ` ` `# least common multiple` ` ` `# of denominators LCD` ` ` `# of 6 and 15 is 30.` ` ` `lcd ` `=` `lcm(den1, den2);` ` ` ` ` `# Computing the numerators` ` ` `# for LCD: Writing 1/6 as` ` ` `# 5/30 and 7/15 as 14/30` ` ` `num1 ` `*` `=` `(lcd ` `/` `den1)` ` ` `num2 ` `*` `=` `(lcd ` `/` `den2)` ` ` `# Our sum is going to be` ` ` `# res_num/lcd` ` ` `res_num ` `=` `num1 ` `+` `num2;` ` ` `print` `( ` `int` `(res_num) , ` `"/"` `,` ` ` `int` `(lcd))` `# Driver Code` `# First fraction is 1/6` `num1 ` `=` `1` `den1 ` `=` `6` `# Second fraction is 7/15` `num2 ` `=` `7` `den2 ` `=` `15` `printSum(num1, den1, num2, den2);` `# This code is contributed` `# by Sam007` |

## C#

`// C# Program to determine LCD of two` `// fractions and Perform addition on` `// fractions` `using` `System;` `class` `GFG {` ` ` `// function to calculate gcd or` ` ` `// hcf of two numbers.` ` ` `static` `int` `gcd(` `int` `a, ` `int` `b)` ` ` `{` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` ` ` `return` `gcd(b % a, a);` ` ` `}` ` ` ` ` `// function to calculate lcm of` ` ` `// two numbers.` ` ` `static` `int` `lcm(` `int` `a, ` `int` `b)` ` ` `{` ` ` `return` `(a * b) / gcd(a, b);` ` ` `}` ` ` ` ` `static` `void` `printSum(` `int` `num1, ` `int` `den1,` ` ` `int` `num2, ` `int` `den2)` ` ` `{` ` ` ` ` `// least common multiple of` ` ` `// denominators LCD of 6 and 15` ` ` `// is 30.` ` ` `int` `lcd = lcm(den1, den2);` ` ` ` ` `// Computing the numerators for LCD:` ` ` `// Writing 1/6 as 5/30 and 7/15 as` ` ` `// 14/30` ` ` `num1 *= (lcd / den1);` ` ` `num2 *= (lcd / den2);` ` ` ` ` `// Our sum is going to be res_num/lcd` ` ` `int` `res_num = num1 + num2;` ` ` ` ` `Console.Write( res_num + ` `"/"` `+ lcd);` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main ()` ` ` `{` ` ` ` ` `// First fraction is 1/6` ` ` `int` `num1 = 1, den1 = 6;` ` ` `// Second fraction is 7/15` ` ` `int` `num2 = 7, den2 = 15;` ` ` `printSum(num1, den1, num2, den2);` ` ` `}` `}` `// This code is contributed by Sam007.` |

## PHP

`<?php` `// PHP Program to determine` `// LCD of two fractions and` `// Perform addition on fractions` `// function to calculate gcd` `// or hcf of two numbers.` `function` `gcd(` `$a` `,` `$b` `)` `{` ` ` `if` `(` `$a` `== 0)` ` ` `return` `$b` `;` ` ` `return` `gcd(` `$b` `% ` `$a` `, ` `$a` `);` `}` `// function to calculate` `// lcm of two numbers.` `function` `lcm(` `$a` `,` `$b` `)` `{` ` ` `return` `(` `$a` `* ` `$b` `) / gcd(` `$a` `, ` `$b` `);` `}` `function` `printSum(` `$num1` `, ` `$den1` `,` ` ` `$num2` `, ` `$den2` `)` `{` ` ` `// least common multiple` ` ` `// of denominators` ` ` `// LCD of 6 and 15 is 30.` ` ` `$lcd` `= lcm(` `$den1` `, ` `$den2` `);` ` ` `// Computing the numerators for LCD:` ` ` `// Writing 1/6 as 5/30 and 7/15 as` ` ` `// 14/30` ` ` `$num1` `*= (` `$lcd` `/ ` `$den1` `);` ` ` `$num2` `*= (` `$lcd` `/ ` `$den2` `);` ` ` `// Our sum is going to be res_num/lcd` ` ` `$res_num` `= ` `$num1` `+ ` `$num2` `;` ` ` `echo` `$res_num` `. ` `"/"` `. ` `$lcd` `;` `}` ` ` `// Driver Code` ` ` `// First fraction is 1/6` ` ` `$num1` `= 1;` ` ` `$den1` `= 6;` ` ` `// Second fraction is 7/15` ` ` `$num2` `= 7;` ` ` `$den2` `= 15;` ` ` `printSum(` `$num1` `, ` `$den1` `, ` `$num2` `, ` `$den2` `);` `// This code is contributed by Sam007.` `?>` |

## Javascript

`<script>` `// javascript Program to determine LCD of two` `// fractions and Perform addition on` `// fractions` ` ` `// function to calculate gcd or` ` ` `// hcf of two numbers.` ` ` `function` `gcd(a , b)` ` ` `{` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `return` `gcd(b % a, a);` ` ` `}` ` ` `// function to calculate lcm of` ` ` `// two numbers.` ` ` `function` `lcm(a , b)` ` ` `{` ` ` `return` `(a * b) / gcd(a, b);` ` ` `}` ` ` `function` `printSum(num1 , den1 , num2 , den2)` ` ` `{` ` ` `// least common multiple of` ` ` `// denominators LCD of 6 and 15` ` ` `// is 30.` ` ` `var` `lcd = lcm(den1, den2);` ` ` `// Computing the numerators for LCD:` ` ` `// Writing 1/6 as 5/30 and 7/15 as` ` ` `// 14/30` ` ` `num1 *= (lcd / den1);` ` ` `num2 *= (lcd / den2);` ` ` `// Our sum is going to be res_num/lcd` ` ` `var` `res_num = num1 + num2;` ` ` `document.write(res_num + ` `"/"` `+ lcd);` ` ` `}` ` ` `// Driver code` ` ` ` ` `// First fraction is 1/6` ` ` `var` `num1 = 1, den1 = 6;` ` ` `// Second fraction is 7/15` ` ` `var` `num2 = 7, den2 = 15;` ` ` `printSum(num1, den1, num2, den2);` `// This code is contributed by todaysgaurav` `</script>` |

**Output :**

19/30

This article is contributed by **Shubham Rana**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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