# Find the largest N digit multiple of N

• Last Updated : 23 Jun, 2021

Given a number N, the task is to find the largest N-digit multiple of N
Examples:

Input: N = 2
Output: 98
Explanation:
98 is the largest multiple of 2 and is of 2 digits.
Input: N = 3
Output: 999
Explanation:
999 is the largest multiple of 3 and is of 3 digits.

Approach: The idea is to make an observation.

• If we observe carefully, a series will be formed as 9, 98, 999, 9996, 99995, …
• In the above series, the N-th term can be calculated as: • 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 largest multiple// of N containing N digits#include #include using namespace std; // Function to find the largest// N digit multiple of N void smallestNumber(int N){    cout << N * floor((pow(10, N) - 1) / N);} // Driver codeint main(){    int N = 2;    smallestNumber(N);     return 0;}

## Java

 // Java program to find largest multiple// of N containing N digitsimport java.util.*;class GFG{ // Function to find the largest// N digit multiple of Nstatic void smallestNumber(int N){    System.out.print(N * Math.floor((                         Math.pow(10, N) - 1) / N));} // Driver codepublic static void main(String args[]){    int N = 2;    smallestNumber(N);}} // This code is contributed by Nidhi_biet

## Python3

 # Python3 program to find largest multiple# of N containing N digitsfrom math import floor # Function to find the largest# N digit multiple of Ndef smallestNumber(N):    print(N * floor((pow(10, N) - 1) / N)) # Driver codeif __name__ == '__main__':    N = 2    smallestNumber(N) # This code is contributed by Mohit Kumar

## C#

 // C# program to find largest multiple// of N containing N digitsusing System;class GFG{ // Function to find the largest// N digit multiple of Nstatic void smallestNumber(int N){    Console.Write(N * Math.Floor((                      Math.Pow(10, N) - 1) / N));} // Driver codepublic static void Main(){    int N = 2;    smallestNumber(N);}} // This code is contributed by Code_Mech

## Javascript

 

Output:

98

Time Complexity: O(1)

Auxiliary Space: O(1)

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