# Maximum sum of distinct numbers such that LCM of these numbers is N

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

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