# Multiple of x closest to n

Given two numbers n and x, we need to calculate the smallest value of x that is closest to given number n.

**Examples:**

Input : n = 9, x = 4 Output : 8 Input : n = 2855, x = 13 Output : 2860 Input : n = 46426171, x = 43 Output : 46426154 Input : n = 1, x = 3 Output : 3

We need to find a k such that x*k is closest to n. If we do k = n/x, we get a value of k that may not lead to maximum. We can get closest by comparing the values floor(n/x) * x and ceil(n/x) * x.

Below is an interesting solution that doesn’t require computations of floor(n/x) and ceil(n/x). The idea is to do following two steps.

n = n + x/2; n = n - (n%x); result = n

Let us consider below example

n = 2855 x = 13 n = 2855 + 13/2 = 2861 n = 2861 - (2861 % 13) = 2861 - 1 = 2860

Below are implementations of above steps.

## C++

`// CPP program to calculate the smallest multiple ` `// of x closest to a given number ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to calculate the smallest multiple ` `int` `closestMultiple(` `int` `n, ` `int` `x) ` `{ ` ` ` `if` `(x>n) ` ` ` `return` `x; ` ` ` ` ` `n = n + x/2; ` ` ` `n = n - (n%x); ` ` ` `return` `n; ` `} ` ` ` `// driver program ` `int` `main() ` `{ ` ` ` `int` `n = 9, x = 4; ` ` ` `printf` `(` `"%d"` `, closestMultiple(n, x)); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to calculate the smallest ` `// multiple of x closest to a given number ` `import` `java.io.*; ` `class` `Solution ` `{ ` ` ` `// Function to calculate the smallest multiple ` ` ` `static` `int` `closestMultiple(` `int` `n, ` `int` `x) ` ` ` `{ ` ` ` `if` `(x>n) ` ` ` `return` `x; ` ` ` `n = n + x/` `2` `; ` ` ` `n = n - (n%x); ` ` ` `return` `n; ` ` ` `} ` ` ` ` ` `// driver program ` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{ ` ` ` `int` `n = ` `56287` `, x = ` `27` `; ` ` ` `System.out.println(closestMultiple(n, x)); ` ` ` `} ` `} ` |

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## Python3

`# Python3 program to calculate ` `# the smallest multiple of x ` `# closest to a given number ` ` ` `# Function to calculate ` `# the smallest multiple ` `def` `closestMultiple(n, x): ` ` ` `if` `x > n: ` ` ` `return` `x; ` ` ` `z ` `=` `(` `int` `)(x ` `/` `2` `); ` ` ` `n ` `=` `n ` `+` `z; ` ` ` `n ` `=` `n ` `-` `(n ` `%` `x); ` ` ` `return` `n; ` ` ` `# Driver Code ` `n ` `=` `56287` `; ` `x ` `=` `27` `; ` `print` `(closestMultiple(n, x)); ` ` ` `# This code is contributed ` `# by mits ` |

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## C#

`// C# program to calculate smallest ` `// multiple of x closest to a ` `// given number ` `using` `System; ` ` ` `class` `Solution { ` ` ` `// Function to calculate the ` ` ` `// smallest multiple ` ` ` `static` `int` `closestMultiple(` `int` `n, ` `int` `x) ` ` ` `{ ` ` ` ` ` `if` `(x > n) ` ` ` `return` `x; ` ` ` `n = n + x / 2; ` ` ` `n = n - (n % x); ` ` ` `return` `n; ` ` ` `} ` ` ` ` ` `// Driver program ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `int` `n = 56287, x = 27; ` ` ` `Console.WriteLine(closestMultiple(n, x)); ` ` ` `} ` `} ` ` ` `// This code is contributed by Anant Agarwal. ` |

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## PHP

`<?php ` `// PHP program to calculate ` `// the smallest multiple ` `// of x closest to a ` `// given number ` ` ` `// Function to calculate ` `// the smallest multiple ` `function` `closestMultiple(` `$n` `, ` `$x` `) ` `{ ` ` ` `if` `(` `$x` `> ` `$n` `) ` ` ` `return` `$x` `; ` ` ` ` ` `$n` `= ` `$n` `+ ` `$x` `/ 2; ` ` ` `$n` `= ` `$n` `- (` `$n` `% ` `$x` `); ` ` ` `return` `$n` `; ` `} ` ` ` ` ` `// Driver Code ` ` ` `$n` `= 9; ` ` ` `$x` `= 4; ` ` ` `echo` `closestMultiple(` `$n` `, ` `$x` `); ` ` ` `// This code is contributed by ajit ` `?> ` |

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**Output:**

56295

This article is contributed by **Pramod Kumar**. 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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