Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

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

  • Last Updated : 27 Jun, 2021

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:
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. 
 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

 



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:
     

N*\lceil 2^\frac{N-1}{N} \rceil
 

  • 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 <iostream>
#include <math.h>
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

Javascript




<script>
// Javascript program to find smallest
// multiple of n with exactly N
// digits in Binary number System.
 
// Function to find smallest multiple
// of n with exactly n digits
// in Binary number representation.
function smallestNumber(N)
{
    document.write(N * parseInt(Math.ceil(Math.pow(2,
                                 (N - 1))
                             / N)));
}
 
// Driver code
let N = 3;
smallestNumber(N);
 
// This code is contributed by rishavmahato348.
</script>
Output: 
6

 

Time Complexity: O(n)
Auxiliary Space: O(1)




My Personal Notes arrow_drop_up
Recommended Articles
Page :