Given a number N. The task is to find the sum of all multiples of 2 and 5 below N ( N may be up to 10^10).

**Examples**:

Input: N = 10Output: 25Explanation: 2 + 4 + 6 + 8 + 5Input: N = 20Output: 110

**Approach :**

We know that multiples of 2 form an AP as:

2, 4, 6, 8, 10, 12, 14….(1)

Similarly, multiples of 5 form an AP as:

5, 10, 15……(2)

Now, **Sum(1) + Sum(2)** = 2, 4, 5, 6, 8, 10, 10, 12, 14, 15….

Here, 10 is repeated. In fact, all of the multiples of 10 or 2*5 are repeated because it is counted twice, once in the series of 2 and again in the series of 5. Hence we’ll subtract the sum of the series of 10 from Sum(1) + Sum(2).

The formula for the sum of an A.P is :

n * ( a + l ) / 2

Where is the number of terms, is the starting term, and is the last term.

So, the Final answer is:

S

_{2}+ S_{5}– S_{10}

Below is the implementation of the above approach:

## C++

`// CPP program to find the sum of all` `// multiples of 2 and 5 below N` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find sum of AP series` `long` `long` `sumAP(` `long` `long` `n, ` `long` `long` `d)` `{` ` ` `// Number of terms` ` ` `n /= d;` ` ` `return` `(n) * (1 + n) * d / 2;` `}` `// Function to find the sum of all` `// multiples of 2 and 5 below N` `long` `long` `sumMultiples(` `long` `long` `n)` `{` ` ` `// Since, we need the sum of` ` ` `// multiples less than N` ` ` `n--;` ` ` `return` `sumAP(n, 2) + sumAP(n, 5) - sumAP(n, 10);` `}` `// Driver code` `int` `main()` `{` ` ` `long` `long` `n = 20;` ` ` `cout << sumMultiples(n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find the sum of all` `// multiples of 2 and 5 below N` `class` `GFG{` `// Function to find sum of AP series` `static` `long` `sumAP(` `long` `n, ` `long` `d)` `{` ` ` `// Number of terms` ` ` `n /= d;` ` ` `return` `(n) * (` `1` `+ n) * d / ` `2` `;` `}` `// Function to find the sum of all` `// multiples of 2 and 5 below N` `static` `long` `sumMultiples(` `long` `n)` `{` ` ` `// Since, we need the sum of` ` ` `// multiples less than N` ` ` `n--;` ` ` `return` `sumAP(n, ` `2` `) + sumAP(n, ` `5` `) - sumAP(n, ` `10` `);` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `long` `n = ` `20` `;` ` ` `System.out.println(sumMultiples(n));` `}` `}` `// This code is contributed by mits` |

## Python3

`# Python3 program to find the sum of` `# all multiples of 2 and 5 below N` `# Function to find sum of AP series` `def` `sumAP(n, d):` ` ` `# Number of terms` ` ` `n ` `=` `int` `(n ` `/` `d);` ` ` `return` `(n) ` `*` `(` `1` `+` `n) ` `*` `(d ` `/` `2` `);` `# Function to find the sum of all` `# multiples of 2 and 5 below N` `def` `sumMultiples(n):` ` ` `# Since, we need the sum of` ` ` `# multiples less than N` ` ` `n ` `-` `=` `1` `;` ` ` `return` `(` `int` `(sumAP(n, ` `2` `) ` `+` `sumAP(n, ` `5` `) ` `-` ` ` `sumAP(n, ` `10` `)));` `# Driver code` `n ` `=` `20` `;` `print` `(sumMultiples(n));` ` ` `# This code is contributed by mits` |

## C#

`// C# program to find the sum of all` `// multiples of 2 and 5 below N` `using` `System;` `public` `class` `GFG{` ` ` ` ` `// Function to find sum of AP series` `static` `long` `sumAP(` `long` `n, ` `long` `d)` `{` ` ` `// Number of terms` ` ` `n /= d;` ` ` `return` `(n) * (1 + n) * d / 2;` `}` `// Function to find the sum of all` `// multiples of 2 and 5 below N` `static` `long` `sumMultiples(` `long` `n)` `{` ` ` `// Since, we need the sum of` ` ` `// multiples less than N` ` ` `n--;` ` ` `return` `sumAP(n, 2) + sumAP(n, 5) - sumAP(n, 10);` `}` `// Driver code` ` ` ` ` `static` `public` `void` `Main (){` ` ` `long` `n = 20;` ` ` `Console.WriteLine(sumMultiples(n));` ` ` `}` `}` |

## PHP

`<?php` `// PHP program to find the sum of all` `// multiples of 2 and 5 below N` `// Function to find sum of AP series` `function` `sumAP(` `$n` `, ` `$d` `)` `{` ` ` `// Number of terms` ` ` `$n` `= (int)(` `$n` `/` `$d` `);` ` ` `return` `(` `$n` `) * ((1 + ` `$n` `) *` ` ` `(int)` `$d` `/ 2);` `}` `// Function to find the sum of all` `// multiples of 2 and 5 below N` `function` `sumMultiples(` `$n` `)` `{` ` ` `// Since, we need the sum of` ` ` `// multiples less than N` ` ` `$n` `--;` ` ` `return` `sumAP(` `$n` `, 2) + sumAP(` `$n` `, 5) -` ` ` `sumAP(` `$n` `, 10);` `}` `// Driver code` `$n` `= 20;` `echo` `sumMultiples(` `$n` `);` `// This code is contributed` `// by Sach_Code` `?>` |

## Javascript

`<script>` `// Java script program to find the sum of all` `// multiples of 2 and 5 below N` `// Function to find sum of AP series` `function` `sumAP(n, d)` `{` ` ` ` ` `// Number of terms` ` ` `n = parseInt(n / d);` ` ` `return` `(n) * ((1 + n) *` ` ` `parseInt(d) / 2);` `}` `// Function to find the sum of all` `// multiples of 2 and 5 below N` `function` `sumMultiples(n)` `{` ` ` ` ` `// Since, we need the sum of` ` ` `// multiples less than N` ` ` `n--;` ` ` `return` `sumAP(n, 2) + sumAP(n, 5) -` ` ` `sumAP(n, 10);` `}` `// Driver code` `n = 20;` `document.write( sumMultiples(n));` `// This code is contributed by bobby` `</script>` |

**Output:**

110

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**

In case you wish to attend live classes with industry experts, please refer **Geeks Classes Live**