# Smallest multiple of N with exactly N digits in its Binary number representation

Given a positive integer N, the task is to find the smallest multiple of N with exactly N digits in its binary number representation.

Example:

Input: N = 3
Output: 6
Explanation:
6 is the smallest multiple of 3 and has length also 3(110) in binary.

Input: N = 5
Output: 20
Explanation:
6 is the smallest multiple of 5 and has length also 5(10100) in binary.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is to make an observation.

• If we observe carefully a series will be formed as 1, 2, 6, 8, 20, …
• The N-th term in the series would be: • Therefore, the number N is taken as the input and the above formula is implemented.

Below is the implementation of the above approach:

## C++

 // C++ program to find smallest  // multiple of n with exactly N  // digits in Binary number System.     #include  #include  using namespace std;     // Function to find smallest multiple  // of n with exactly n digits  // in Binary number representation.  void smallestNumber(int N)  {      cout << N * ceil(pow(2,                           (N - 1))                       / N);  }     // Driver code  int main()  {      int N = 3;      smallestNumber(N);         return 0;  }

## Java

 // Java program to find smallest   // multiple of n with exactly N   // digits in Binary Number System.   class GFG{      // Function to find smallest   // multiple of n with exactly N   // digits in Binary Number System.   static void smallestNumber(int N)   {       System.out.print(N * Math.ceil                          (Math.pow(2, (N - 1)) / N));   }      // Driver code   public static void main(String[] args)   {       int N = 3;              smallestNumber(N);  }   }      // This code is contributed by shubham

## Python3

 # Python3 program to find smallest  # multiple of n with exactly N  # digits in Binary number System.  from math import ceil     # Function to find smallest multiple  # of n with exactly n digits  # in Binary number representation.  def smallestNumber(N):      print(N * ceil(pow(2, (N - 1)) / N))     # Driver code  N = 3 smallestNumber(N)     # This code is contributed by Mohit Kumar

## C#

 // C# program to find smallest   // multiple of n with exactly N   // digits in Binary Number System.  using System;     class GFG{      // Function to find smallest   // multiple of n with exactly N   // digits in Binary Number System.   static void smallestNumber(int N)   {       Console.Write(N * Math.Ceiling(                        Math.Pow(2, (N - 1)) / N));   }          // Driver code   public static void Main(string[] args)   {       int N = 3;                  smallestNumber(N);  }   }      // This code is contributed by AnkitRai01

Output:

6


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