Integers X and K are given. The task is to find the smallest K-digit number divisible by X.

**Examples :**

Input : X = 83, K = 5 Output : 10043 10040 is the smallest 5 digit number that is multiple of 83. Input : X = 5, K = 2 Output : 10

A **simple solution** is to try all numbers starting from the smallest K digit number

(which is 100…(K-1)times) and return the first number divisible by X.

An **efficient solution** would be :

Compute MIN : smallest K-digit number (1000...(K-1)times) If, MIN % X is 0, ans = MIN else, ans = (MIN + X) - ((MIN + X) % X)) This is because there will be a number in range [MIN...MIN+X] divisible by X.

## C++

`// C++ code to find smallest K-digit number` `// divisible by X` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to compute the result` `int` `answer(` `int` `X, ` `int` `K)` `{` ` ` `// Computing MIN` ` ` `int` `MIN = ` `pow` `(10, K - 1);` ` ` `// MIN is the result` ` ` `if` `(MIN % X == 0)` ` ` `return` `MIN;` ` ` `// returning ans` ` ` `return` `((MIN + X) - ((MIN + X) % X));` `}` `// Driver Code` `int` `main()` `{` ` ` `// Number whose divisible is to be found` ` ` `int` `X = 83;` ` ` `// Max K-digit divisible is to be found` ` ` `int` `K = 5;` ` ` `cout << answer(X, K);` `}` |

## Java

`// Java code to find smallest K-digit` `// number divisible by X` `import` `java.io.*;` `import` `java.lang.*;` `class` `GFG {` ` ` `public` `static` `double` `answer(` `double` `X, ` `double` `K)` ` ` `{` ` ` `double` `i = ` `10` `;` ` ` `// Computing MIN` ` ` `double` `MIN = Math.pow(i, K - ` `1` `);` ` ` `// returning ans` ` ` `if` `(MIN % X == ` `0` `)` ` ` `return` `(MIN);` ` ` `else` ` ` `return` `((MIN + X) - ((MIN + X) % X));` ` ` `}` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `// Number whose divisible is to be found` ` ` `double` `X = ` `83` `;` ` ` `double` `K = ` `5` `;` ` ` `System.out.println((` `int` `)answer(X, K));` ` ` `}` `}` `// Code contributed by Mohit Gupta_OMG <(0_o)>` |

## Python3

`# Python code to find smallest K-digit ` `# number divisible by X` `def` `answer(X, K):` ` ` ` ` `# Computing MAX` ` ` `MIN` `=` `pow` `(` `10` `, K` `-` `1` `)` ` ` ` ` `if` `(` `MIN` `%` `X ` `=` `=` `0` `):` ` ` `return` `(` `MIN` `)` ` ` ` ` `else` `:` ` ` `return` `((` `MIN` `+` `X) ` `-` `((` `MIN` `+` `X) ` `%` `X))` ` ` `X ` `=` `83` `;` `K ` `=` `5` `;` `print` `(answer(X, K));` `# Code contributed by Mohit Gupta_OMG <(0_o)>` |

## C#

`// C# code to find smallest K-digit` `// number divisible by X` `using` `System;` `class` `GFG {` ` ` `// Function to compute the result` ` ` `public` `static` `double` `answer(` `double` `X, ` `double` `K)` ` ` `{` ` ` `double` `i = 10;` ` ` `// Computing MIN` ` ` `double` `MIN = Math.Pow(i, K - 1);` ` ` `// returning ans` ` ` `if` `(MIN % X == 0)` ` ` `return` `MIN;` ` ` `else` ` ` `return` `((MIN + X) - ((MIN + X) % X));` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `// Number whose divisible is to be found` ` ` `double` `X = 83;` ` ` `double` `K = 5;` ` ` `Console.WriteLine((` `int` `)answer(X, K));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP code to find smallest` `// K-digit number divisible by X` `// Function to compute` `// the result` `function` `answer(` `$X` `, ` `$K` `)` `{` ` ` `// Computing MIN` ` ` `$MIN` `= pow(10, ` `$K` `- 1);` ` ` `// MIN is the result` ` ` `if` `(` `$MIN` `% ` `$X` `== 0)` ` ` `return` `$MIN` `;` ` ` `// returning ans` ` ` `return` `((` `$MIN` `+ ` `$X` `) -` ` ` `((` `$MIN` `+ ` `$X` `) % ` `$X` `));` `}` `// Driver Code` `// Number whose divisible` `// is to be found` `$X` `= 83;` `// Max K-digit divisible` `// is to be found` `$K` `= 5;` `echo` `answer(` `$X` `, ` `$K` `);` `// This code is contributed by ajit` `?>` |

## Javascript

`<script>` `// Javascript code to find smallest` `// K-digit number divisible by X` `// Function to compute` `// the result` `function` `answer(X, K)` `{` ` ` ` ` `// Computing MIN` ` ` `let MIN = Math.pow(10, K - 1);` ` ` `// MIN is the result` ` ` `if` `(MIN % X == 0)` ` ` `return` `MIN;` ` ` `// returning ans` ` ` `return` `((MIN + X) -` ` ` `((MIN + X) % X));` `}` `// Driver Code` `// Number whose divisible` `// is to be found` `let X = 83;` `// Max K-digit divisible` `// is to be found` `let K = 5;` `document.write(answer(X, K));` ` ` `// This code is contributed by sravan kumar` `</script>` |

**Output :**

10043

This article is contributed by **Rohit Thapliyal**. 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.

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the **Essential Maths for CP Course** at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**