El mínimo común denominador o mínimo común denominador es el mínimo común múltiplo de los denominadores de un conjunto de fracciones.
Denominador común : cuando los denominadores de dos o más fracciones son iguales.
El mínimo común denominador es el más pequeño de todos los denominadores comunes.
¿Por qué necesitamos LCD ?
Simplifica la suma, la resta y la comparación de fracciones.
El denominador común se puede evaluar simplemente multiplicando los denominadores. En este caso, 3 * 6 = 18
Pero ese puede no ser siempre el mínimo común denominador, como en este caso LCD = 6 y no 18. LCD es en realidad MCM de denominadores.
Ejemplos:
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.
Problema de ejemplo: dadas dos fracciones, encuentra su suma usando el mínimo común dominador.
Ejemplos :
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
Nota* Estas respuestas se pueden simplificar aún más mediante la cancelación anómala.
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>
Producción :
19/30
Complejidad de tiempo: O(log(max(deno1,deno2)))
Espacio auxiliar: O(log(max(deno1,deno2)))
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Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA