# Java Program for 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

An **efficient solution** would be :

Compute MIN : smallest K-digit number (1000...K-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.

`// 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)> ` |

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**Output:**

10043

To understand Math.pow() function, please refer point 18 of the article :

https://www.geeksforgeeks.org/java-lang-math-class-java-set-2/

Please refer complete article on Smallest K digit number divisible by X for more details!

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