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Maximum sum of distinct numbers such that LCM of these numbers is N
  • Difficulty Level : Medium
  • Last Updated : 22 Mar, 2021

Given a positive number N. The task is to find maximum sum of distinct numbers such that the LCM of all these numbers is equal to N.
Examples: 
 

Input  : 2
Output : 3
The distinct numbers you can have are 
just 1 and 2 and their sum is equal to 3.

Input  : 5
Output : 6

 

As the LCM of all the numbers is N. So all the numbers must be the divisors of N and all the numbers are distinct so answer must be the sum of all the divisors of N. To find all the divisors efficiently refer to article https://www.geeksforgeeks.org/find-all-divisors-of-a-natural-number-set-2/
 

C++




// C++ program to find the max sum of
// numbers whose lcm is n
#include<bits/stdc++.h>
using namespace std;
 
// Returns maximum sum of numbers with
// LCM as N
int maxSumLCM(int n)
{
    int max_sum = 0;  // Initialize result
 
    // Finding a divisor of n and adding
    // it to max_sum
    for (int i=1; i*i<=n; i++)
    {
        if (n%i == 0)
        {
            max_sum += i;
            if (n/i != i)
                max_sum += (n/i);
        }
    }
 
    return max_sum;
}
 
// Driver code
int main()
{
    int n = 2;
    cout << MaxSumLCM(n) << endl;
    return 0;
}

Java




// Java program to find the max sum of
// numbers whose lcm is n
 
class MaxSum
{
    // Returns maximum sum of numbers with
    // LCM as N
    static int maxSumLCM(int n)
    {
        int max_sum = 0// Initialize result
      
        // Finding a divisor of n and adding
        // it to max_sum
        for (int i=1; i*i<=n; i++)
        {
            if (n%i == 0)
            {
                max_sum += i;
                if (n/i != i)
                    max_sum += (n/i);
            }
        }
         
        return max_sum;
    }
     
    // main function
    public static void main (String[] args)
    {
        int n = 2;
        System.out.println(maxSumLCM(n));
    }
}

Python3




# Python3 program to find the max sum of
# numbers whose lcm is n
 
# Returns maximum sum of numbers with
# LCM as N
def maxSumLCM(n) :
     
    # Initialize result
    max_sum = 0
 
    # Finding a divisor of n and adding
    # it to max_sum
    i = 1
    while(i * i<= n ):
        if (n % i == 0) :
            max_sum = max_sum + i
            if (n // i != i) :
                max_sum = max_sum + (n // i)
        i = i + 1
     
    return max_sum
 
# Driver code
n = 2
print(maxSumLCM(n))
 
# This code is contributed by Nikita Tiwari.

C#




// C# program to find the max sum
// of numbers whose lcm is n
using System;
 
class MaxSum
{
     
    // Returns maximum sum of 
    // numbers with LCM as N
    static int maxSumLCM(int n)
    {
         
         // Initialize result
         int max_sum = 0;
     
        // Finding a divisor of n and
        // adding it to max_sum
        for (int i = 1; i * i <= n; i++)
        {
            if (n % i == 0)
            {
                max_sum += i;
                if (n / i != i)
                    max_sum += (n / i);
            }
        }
         
        return max_sum;
    }
     
    // Driver Code
    public static void Main (String[] args)
    {
        int n = 2;
        Console.Write(maxSumLCM(n));
    }
}
 
// This code is contributed by parashar..

PHP




<?php
// PHP program to find
// the max sum of numbers
// whose lcm is n
 
// Returns maximum sum
// of numbers with
// LCM as N
function maxSumLCM($n)
{
    // Initialize result
    $max_sum = 0;
 
    // Finding a divisor
    // of n and adding
    // it to max_sum
    for ($i = 1;
         $i * $i <= $n; $i++)
    {
        if ($n % $i == 0)
        {
            $max_sum += $i;
            if ($n / $i != $i)
                $max_sum += ($n / $i);
        }
    }
 
    return $max_sum;
}
 
// Driver code
$n = 2;
echo MaxSumLCM($n);
     
// This code is contributed
// by ajit
?>

Javascript




<script>
 
// Javascript program to find the max sum of
// numbers whose lcm is n
 
// Returns maximum sum of numbers with
// LCM as N
function maxSumLCM(n)
{
    let max_sum = 0; // Initialize result
 
    // Finding a divisor of n and adding
    // it to max_sum
    for (let i=1; i*i<=n; i++)
    {
        if (n%i == 0)
        {
            max_sum += i;
            if (n/i != i)
                max_sum += (n/i);
        }
    }
 
    return max_sum;
}
 
// Driver code
  
    let n = 2;
    document.write(maxSumLCM(n) + "<br>");
     
// This code is contributed by Mayank Tyagi
 
</script>

Output: 

3

This article is contributed by Ayush Jha. 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.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 

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