# 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.

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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 codeint 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 codepublic 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 codeN = 3smallestNumber(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 codepublic static void Main(string[] args){    int N = 3;             smallestNumber(N);}} // This code is contributed by AnkitRai01

## Javascript

 
Output:
6

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

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