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# 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.

#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.

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