How to Find the Lcm of Two Numbers
LCM (Least Common Multiple) of two numbers is the smallest number which can be divided by both numbers.
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For example, LCM of 15 and 20 is 60, and LCM of 5 and 7 is 35.
A simple solution is to find all prime factors of both numbers, then find union of all factors present in both numbers. Finally, return the product of elements in union.
An efficient solution is based on the below formula for LCM of two numbers 'a' and 'b'.
a x b = LCM(a, b) * GCD (a, b) LCM(a, b) = (a x b) / GCD(a, b)
We have discussed function to find GCD of two numbers. Using GCD, we can find LCM.
Below is the implementation of the above idea:
C++
#include <iostream>
using namespace std;
long long gcd( long long int a, long long int b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}
long long lcm( int a, int b)
{
return (a / gcd(a, b)) * b;
}
int main()
{
int a = 15, b = 20;
cout << "LCM of " << a << " and "
<< b << " is " << lcm(a, b);
return 0;
}
C
#include <stdio.h>
int gcd( int a, int b)
{
if (a == 0)
return b;
return gcd(b % a, a);
}
int lcm( int a, int b)
{
return (a / gcd(a, b)) * b;
}
int main()
{
int a = 15, b = 20;
printf ( "LCM of %d and %d is %d " , a, b, lcm(a, b));
return 0;
}
Java
class Test
{
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 / gcd(a, b)) * b;
}
public static void main(String[] args)
{
int a = 15 , b = 20 ;
System.out.println( "LCM of " + a +
" and " + b +
" is " + lcm(a, b));
}
}
Python3
def gcd(a,b):
if a = = 0 :
return b
return gcd(b % a, a)
def lcm(a,b):
return (a / gcd(a,b)) * b
a = 15
b = 20
print ( 'LCM of' , a, 'and' , b, 'is' , lcm(a, b))
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 / gcd(a, b)) * b;
}
public static void Main()
{
int a = 15, b = 20;
Console.WriteLine( "LCM of " + a +
" and " + b + " is " + lcm(a, b));
}
}
PHP
<?php
function gcd( $a , $b )
{
if ( $a == 0)
return $b ;
return gcd( $b % $a , $a );
}
function lcm( $a , $b )
{
return ( $a / gcd( $a , $b )) * $b ;
}
$a = 15;
$b = 20;
echo "LCM of " , $a , " and "
, $b , " is " , lcm( $a , $b );
?>
Javascript
<script>
function gcd(a, b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}
function lcm(a, b)
{
return (a / gcd(a, b)) * b;
}
let a = 15, b = 20;
document.write( "LCM of " + a + " and "
+ b + " is " + lcm(a, b));
</script>
Output
LCM of 15 and 20 is 60
Time Complexity: O(log(max(a,b))
Auxiliary Space: O(log(max(a,b))
https://youtu.be/anSfYgbo694
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How to Find the Lcm of Two Numbers
Source: https://www.geeksforgeeks.org/program-to-find-lcm-of-two-numbers/