Largest N digit number divisible by given three numbers in C++

In this tutorial, we are going to write a program that finds the largest n-digit number that is divisible by the given three numbers.

Let's see the steps to solve the problem.

• Initialise three numbers along with n.
• Find the LCM of three numbers.
• Store the largest number with n-digits.
• If the largest number is divisible by n, then return it.
• Else check for the number obtained from subtracting remainder in the above step.

Example

Let's see the code.

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int LCM(int x, int y, int z) {
   int ans = ((x * y) / (__gcd(x, y)));
   return ((z * ans) / (__gcd(ans, z)));
}
int findNumber(int n, int x, int y, int z) {
   int lcm = LCM(x, y, z);
   int largestNDigitNumber = pow(10, n) - 1;
   int remainder = largestNDigitNumber % lcm;
   if (remainder == 0) {
      return largestNDigitNumber;
   }
   largestNDigitNumber -= remainder;
   if (largestNDigitNumber >= pow(10, n - 1)) {
      return largestNDigitNumber;
   }
   return 0;
}
int main() {
   int n = 4, x = 6, y = 7, z = 8;
   int result = findNumber(n, x, y, z);
   if (result != 0) {
      cout << result << endl;
   }else {
      cout << "Not possible" << endl;
   }
   return 0;
}

Output

If you run the above code, then you will get the following result.

9912

Conclusion

If you have any queries in the tutorial, mention them in the comment section.

Hafeezul Kareem

Published on 09-Apr-2021 13:29:45