# Smallest number divisible by n and has at-least k trailing zeros

Two integers n and k are given. Our task is to print K-rounding of n. K-rounding is the minimum positive integer X, such that x ends with k or more zeros and is divisible by n.**Examples :**

Input : n = 30, k = 3. Output : 3000 3000 is the smallest number that has at-least k 0s and is divisible by n. Input : n = 375, k = 4. Output : 30000

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**Method 1 :**

The brute force approach is to start with result = 10^{k}. Check if result is divided by n. If yes, it’s the answer, else increase it by 10^{k}**Method 2 :** The efficient approach is to calculate the LCM of 10^{k} and n.

Suppose, n = 375, k = 4.

result = 10000.

Now, LCM of 375 and 10000 is the lowest number divided by both of them.

It will contain k or more zeros (because it is multiple of 10^{k}) and will be a multiple of n as well.

Below is the implementation :

## C++

`// CPP code to print K-rounded value of n` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to compute the rounded value` `long` `long` `getRounding(` `long` `long` `n, ` `long` `long` `k)` `{` ` ` `long` `long` `rounding = ` `pow` `(10, k);` ` ` `// Computing GCD` ` ` `long` `long` `result = __gcd(rounding, n);` ` ` `// Returning LCM (GCD * LCM = n * k)` ` ` `return` `((rounding * n) / result);` `}` `// Driver Code` `int` `main()` `{` ` ` `long` `long` `n = 375, k = 4;` ` ` `// Function call` ` ` `cout << getRounding(n, k);` ` ` `return` `0;` `}` |

## Java

`// JAVA Code For Smallest number divisible by` `// n and has at-least k trailing zeros` `import` `java.util.*;` `class` `GFG {` ` ` ` ` `// Function to find gcd` ` ` `static` `long` `gcd(` `long` `a, ` `long` `b)` ` ` `{` ` ` `// Everything divides 0` ` ` `if` `(a == ` `0` `|| b == ` `0` `)` ` ` `return` `0` `;` ` ` ` ` `// base case` ` ` `if` `(a == b)` ` ` `return` `a;` ` ` ` ` `// a is greater` ` ` `if` `(a > b)` ` ` `return` `gcd(a-b, b);` ` ` `return` `gcd(a, b-a);` ` ` `}` ` ` `// Function to compute the rounded value` ` ` `public` `static` `long` `getRounding(` `long` `n, ` `long` `k)` ` ` `{` ` ` `long` `rounding = (` `long` `)Math.pow(` `10` `, k);` ` ` ` ` `// Computing GCD` ` ` `long` `result = gcd(rounding, n);` ` ` ` ` `// Returning LCM (GCD * LCM = n * k)` ` ` `return` `((rounding * n) / result);` ` ` `}` ` ` ` ` `/* Driver program to test above function */` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `long` `n = ` `375` `, k = ` `4` `;` ` ` ` ` `// Function call` ` ` `System.out.println( getRounding(n, k));` ` ` ` ` `}` `}` ` ` `// This code is contributed by Arnav Kr. Mandal.` |

## Python3

`# python Code For Smallest number` `# divisible by n and has` `# at-least k trailing zeros` `# Function to find gcd` `def` `gcd(a, b):` ` ` ` ` `# Everything divides 0` ` ` `if` `(a ` `=` `=` `0` `or` `b ` `=` `=` `0` `):` ` ` `return` `0` ` ` ` ` `# base case` ` ` `if` `(a ` `=` `=` `b):` ` ` `return` `a` ` ` ` ` `# a is greater` ` ` `if` `(a > b):` ` ` `return` `gcd(a ` `-` `b, b)` ` ` ` ` `return` `gcd(a, b ` `-` `a)` ` ` `# Function to compute the` `# rounded value` `def` `getRounding(n, k):` ` ` ` ` `rounding ` `=` `pow` `(` `10` `, k);` ` ` `# Computing GCD` ` ` `result ` `=` `gcd(rounding, n)` ` ` `# Returning LCM (GCD * LCM` ` ` `# = n * k)` ` ` `return` `((rounding ` `*` `n) ` `/` `result)` `# Driver Code` `n ` `=` `375` `k ` `=` `4` `# Function call` `print` `( ` `int` `(getRounding(n, k)))` `# This code is contributed by Sam007` |

## C#

`// C# Code For Smallest number` `// divisible by n and has` `// at-least k trailing zeros` `using` `System;` `class` `GFG {` ` ` ` ` `// Function to find gcd` ` ` `static` `long` `gcd(` `long` `a, ` `long` `b)` ` ` `{` ` ` ` ` `// Everything divides 0` ` ` `if` `(a == 0 || b == 0)` ` ` `return` `0;` ` ` ` ` `// base case` ` ` `if` `(a == b)` ` ` `return` `a;` ` ` ` ` `// a is greater` ` ` `if` `(a > b)` ` ` `return` `gcd(a - b, b);` ` ` `return` `gcd(a, b - a);` ` ` `}` ` ` `// Function to compute the rounded value` ` ` `public` `static` `long` `getRounding(` `long` `n, ` `long` `k)` ` ` `{` ` ` `long` `rounding = (` `long` `)Math.Pow(10, k);` ` ` ` ` `// Computing GCD` ` ` `long` `result = gcd(rounding, n);` ` ` ` ` `// Returning LCM (GCD * LCM = n * k)` ` ` `return` `((rounding * n) / result);` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `long` `n = 375, k = 4;` ` ` ` ` `// Function call` ` ` `Console.Write( getRounding(n, k));` ` ` ` ` `}` `}` ` ` `// This code is contributed by Nitin Mittal.` |

## PHP

`<?php` `// PHP Code For Smallest number` `// divisible by n and has` `// at-least k trailing zeros` `function` `gcd(` `$a` `, ` `$b` `)` `{` ` ` ` ` `// Everything divides 0` ` ` `if` `(` `$a` `== 0 || ` `$b` `== 0)` ` ` `return` `0;` ` ` ` ` `// base case` ` ` `if` `(` `$a` `== ` `$b` `)` ` ` `return` `$a` `;` ` ` ` ` `// a is greater` ` ` `if` `(` `$a` `> ` `$b` `)` ` ` `return` `gcd(` `$a` `- ` `$b` `, ` `$b` `);` ` ` `return` `gcd(` `$a` `, ` `$b` `- ` `$a` `);` `}` `// Function to compute` `// the rounded value` `function` `getRounding(` `$n` `, ` `$k` `)` `{` ` ` `$rounding` `= ` `intval` `(pow(10, ` `$k` `));` ` ` `// Computing GCD` ` ` `$result` `= gcd(` `$rounding` `, ` `$n` `);` ` ` `// Returning LCM (GCD * LCM = n * k)` ` ` `return` `intval` `((` `$rounding` `* ` `$n` `) /` ` ` `$result` `);` `}` `// Driver code` `$n` `= 375;` `$k` `= 4;` `// Function call` `echo` `getRounding(` `$n` `, ` `$k` `);` `// This code is contributed by Sam007` `?>` |

## Javascript

`<script>` `// javascript Code For Smallest number divisible by` `// n and has at-least k trailing zeros` ` ` `// Function to find gcd` ` ` `function` `gcd(a , b)` ` ` `{` ` ` ` ` `// Everything divides 0` ` ` `if` `(a == 0 || b == 0)` ` ` `return` `0;` ` ` `// base case` ` ` `if` `(a == b)` ` ` `return` `a;` ` ` `// a is greater` ` ` `if` `(a > b)` ` ` `return` `gcd(a - b, b);` ` ` `return` `gcd(a, b - a);` ` ` `}` ` ` `// Function to compute the rounded value` ` ` `function` `getRounding(n , k)` ` ` `{` ` ` `var` `rounding = Math.pow(10, k);` ` ` `// Computing GCD` ` ` `var` `result = gcd(rounding, n);` ` ` `// Returning LCM (GCD * LCM = n * k)` ` ` `return` `((rounding * n) / result);` ` ` `}` ` ` `/* Driver program to test above function */` ` ` `var` `n = 375, k = 4;` ` ` `// Function call` ` ` `document.write(getRounding(n, k));` `// This code is contributed by todaysgaurav` `</script>` |

**Output :**

30000

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