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Smallest K digit number divisible by X
  • Difficulty Level : Easy
  • Last Updated : 07 Apr, 2021

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.
 

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