# Smallest K digit number divisible by X

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
```

## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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.
```

## CPP

 `// CPP code to find smallest K-digit number ` `// divisible by X ` `#include ` `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

 ` `

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.

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