Given a number a and limit N. Find the sum of multiple of a upto N.

**Examples :**

Input : a = 4, N = 23 Output : sum = 60 [Multiples : 4, 8, 12, 16, 20] Input :a = 7, N = 49 Output :sum = 196 [Multiples: 7, 14, 21, 28, 35, 42, 49]

The basic idea is to iterate from i = a to i = n, i++ and check whether i % a == 0 or not.If zero then add i to sum(initially sum = 0).Thus we will get the sum.It will take O(n) time.

We can modify the loop as i = a, i <= n, i = i + a to reduce the number of iterations.But it will also take O(m) time if there is m multiples of a.

To get the result in O(1) time we can use the formula of summation of n natural numbers.For the above example,

a = 4 and N = 23, number of multiples of a, m = N/a(integer division). The multiples are 4, 8, 12, 16, 20.

We can write it as 4 X [1, 2, 3, 4, 5]. So we can get the sum of multiples as:

sum = a * (Summation of 1 to m [natural numbers from 1 to m]) sum = 4 * (m*(m+1) / 2) sum = 4 * (5*6 / 2) = 4 * 15 = 60

## C++

`// C++ program to find sum of multiples of a number` `// up to N efficiently` `#include <iostream>` `using` `namespace` `std;` `// Function for calculating sum of multiples of` `// a upto N` `int` `calculate_sum(` `int` `a, ` `int` `N)` `{` ` ` `// Number of multiples` ` ` `int` `m = N / a;` ` ` `// sum of first m natural numbers` ` ` `int` `sum = m * (m + 1) / 2;` ` ` `// sum of multiples` ` ` `int` `ans = a * sum;` ` ` `return` `ans;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `a = 7, N = 49;` ` ` `cout << ` `"Sum of multiples of "` ` ` `<< a << ` `" up to "` `<< N << ` `" = "` ` ` `<< calculate_sum(a, N) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program to find sum of multiples` `// of a number up to N efficiently` `class` `GFG {` ` ` `// Function for calculating sum` `// of multiples of a upto N` `static` `int` `calculate_sum(` `int` `a, ` `int` `N) {` ` ` ` ` `// Number of multiples` ` ` `int` `m = N / a;` ` ` `// sum of first m natural numbers` ` ` `int` `sum = m * (m + ` `1` `) / ` `2` `;` ` ` `// sum of multiples` ` ` `int` `ans = a * sum;` ` ` `return` `ans;` `}` `// Driver code` `public` `static` `void` `main(String[] args) {` ` ` ` ` `int` `a = ` `7` `, N = ` `49` `;` ` ` `System.out.println(` `"Sum of multiples of "` `+ a +` ` ` `" up to "` `+ N + ` `" = "` `+` ` ` `calculate_sum(a, N));` `}` `}` `// This code is contributed by Anant Agarwal.` |

## Python3

`"""Python program to find sum of` `multiples of a number up to N"""` `# Calculates sum of multiples of` `# a number upto N` `def` `calculate_sum(a, N):` ` ` `# Number of multiples` ` ` `m ` `=` `N ` `/` `a` ` ` `# sum of first m natural numbers` ` ` `sum` `=` `m ` `*` `(m ` `+` `1` `) ` `/` `2` ` ` `# sum of multiples` ` ` `ans ` `=` `a ` `*` `sum` ` ` `print` `(` `"Sum of multiples of "` `, a,` ` ` `" up to "` `, N, ` `" = "` `, ans)` `# Driver Code` `calculate_sum(` `7` `, ` `49` `)` ` ` `# This code is contributed by Abhishek Agrawal.` |

## C#

`// C# program to find sum of multiples` `// of a number up to N efficiently` `using` `System;` `class` `GFG {` ` ` `// Function for calculating sum` ` ` `// of multiples of a upto N` ` ` `static` `int` `calculate_sum(` `int` `a, ` `int` `N)` ` ` `{` ` ` `// Number of multiples` ` ` `int` `m = N / a;` ` ` `// sum of first m natural numbers` ` ` `int` `sum = m * (m + 1) / 2;` ` ` `// sum of multiples` ` ` `int` `ans = a * sum;` ` ` `return` `ans;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `a = 7, N = 49;` ` ` `Console.WriteLine(` `"Sum of multiples of "` `+ a +` ` ` `" up to "` `+ N + ` `" = "` `+ calculate_sum(a, N));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find sum` `// of multiples of a number` `// up to N efficiently` `// Function for calculating sum` `// of multiples of a upto N` `function` `calculate_sum(` `$a` `, ` `$N` `)` `{` ` ` `// Number of multiples` ` ` `$m` `= ` `$N` `/ ` `$a` `;` ` ` `// sum of first m` ` ` `// natural numbers` ` ` `$sum` `= ` `$m` `* (` `$m` `+ 1) / 2;` ` ` `// sum of multiples` ` ` `$ans` `= ` `$a` `* ` `$sum` `;` ` ` `return` `$ans` `;` `}` `// Driver code` `$a` `= 7;` `$N` `= 49;` `echo` `"Sum of multiples of "` `. ` `$a` `,` ` ` `" up to "` `. ` `$N` `. ` `" = "` `.` ` ` `calculate_sum(` `$a` `, ` `$N` `) ;` `// This code is contributed by Sam007` `?>` |

## Javascript

`<script>` `// Javascript program to find sum` `// of multiples of a number` `// up to N efficiently` `// Function for calculating sum` `// of multiples of a upto N` `function` `calculate_sum(a, N)` `{` ` ` ` ` `// Number of multiples` ` ` `m = N / a;` ` ` `// Sum of first m` ` ` `// natural numbers` ` ` `sum = m * (m + 1) / 2;` ` ` `// Sum of multiples` ` ` `ans = a * sum;` ` ` `return` `ans;` `}` `// Driver code` `let a = 7;` `let N = 49;` `document.write(` `"Sum of multiples of "` `+ a +` ` ` `" up to "` `+ N + ` `" = "` `+` ` ` `calculate_sum(a, N));` `// This code is contributed by mohan1240760` `</script>` |

**Output : **

Sum of multiples of 7 upto 49 = 196

This article is contributed by **Sukanta Nandi**. 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.

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