How To Get X Out Of The Denominator

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

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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++

#include <iostream>

using namespace std;

int gcd( int a, int b)

{

if (a == 0)

return b;

return gcd(b % a, a);

}

int lcm( int a, int b)

{

return (a * b) / gcd(a, b);

}

void printSum( int num1, int den1,

int num2, int den2)

{

int lcd = lcm(den1, den2);

num1 *= (lcd / den1);

num2 *= (lcd / den2);

int res_num = num1 + num2;

cout << res_num << "/" << lcd;

}

int main()

{

int num1 = 1, den1 = 6;

int num2 = 7, den2 = 15;

printSum(num1, den1, num2, den2);

return 0;

}

Java

public class GFG {

static int gcd( int a, int b)

{

if (a == 0 )

return b;

return gcd(b % a, a);

}

static int lcm( int a, int b)

{

return (a * b) / gcd(a, b);

}

static void printSum( int num1, int den1,

int num2, int den2)

{

int lcd = lcm(den1, den2);

num1 *= (lcd / den1);

num2 *= (lcd / den2);

int res_num = num1 + num2;

System.out.print( res_num + "/" + lcd);

}

public static void main(String args[])

{

int num1 = 1 , den1 = 6 ;

int num2 = 7 , den2 = 15 ;

printSum(num1, den1, num2, den2);

}

Python3

def gcd(a, b):

if (a = = 0 ):

return b

return gcd(b % a, a)

def lcm(a, b):

return (a * b) / gcd(a, b)

def printSum(num1, den1,

num2, den2):

lcd = lcm(den1, den2);

num1 * = (lcd / den1)

num2 * = (lcd / den2)

res_num = num1 + num2;

print ( int (res_num) , "/" ,

int (lcd))

num1 = 1

den1 = 6

num2 = 7

den2 = 15

printSum(num1, den1, num2, den2);

C#

using System;

class GFG {

static int gcd( int a, int b)

{

if (a == 0)

return b;

return gcd(b % a, a);

}

static int lcm( int a, int b)

{

return (a * b) / gcd(a, b);

}

static void printSum( int num1, int den1,

int num2, int den2)

{

int lcd = lcm(den1, den2);

num1 *= (lcd / den1);

num2 *= (lcd / den2);

int res_num = num1 + num2;

Console.Write( res_num + "/" + lcd);

}

public static void Main ()

{

int num1 = 1, den1 = 6;

int num2 = 7, den2 = 15;

printSum(num1, den1, num2, den2);

}

PHP

<?php

function gcd( $a , $b )

{

if ( $a == 0)

return $b ;

return gcd( $b % $a , $a );

}

function lcm( $a , $b )

{

return ( $a * $b ) / gcd( $a , $b );

}

function printSum( $num1 , $den1 ,

$num2 , $den2 )

{

$lcd = lcm( $den1 , $den2 );

$num1 *= ( $lcd / $den1 );

$num2 *= ( $lcd / $den2 );

$res_num = $num1 + $num2 ;

echo $res_num . "/" . $lcd ;

}

$num1 = 1;

$den1 = 6;

$num2 = 7;

$den2 = 15;

printSum( $num1 , $den1 , $num2 , $den2 );

?>

Javascript

<script>

function gcd(a , b)

{

if (a == 0)

return b;

return gcd(b % a, a);

}

function lcm(a , b)

{

return (a * b) / gcd(a, b);

}

function printSum(num1 , den1 , num2 , den2)

{

var lcd = lcm(den1, den2);

num1 *= (lcd / den1);

num2 *= (lcd / den2);

var res_num = num1 + num2;

document.write(res_num + "/" + lcd);

}

var num1 = 1, den1 = 6;

var num2 = 7, den2 = 15;

printSum(num1, den1, num2, den2);

</script>

Output :

19/30

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