Given two integer p and q, the task is to find the minimum possible number x such that q % x = 0 and x % p = 0. If the conditions aren’t true for any number then print -1.
Examples:
Input: p = 3, q = 99
Output: 3
99 % 3 = 0
3 % 3 = 0Input: p = 2, q = 7
Output: -1
Approach: If a number x satisfies the given condition then it’s obvious that q will be divided by p i.e. q % p = 0 because x is a multiple of p and q is a multiple of x.
So the minimum possible value of x will be the GCD of p and q and when q is not divisible by p then no number will satisfy the given condition.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function to return the minimum valid number // that satisfies the given conditions int minValidNumber(int p, int q) { // If possible if (q % p == 0) return __gcd(p, q); else return -1; } // Driver Code int main() { int p = 2, q = 6; cout << minValidNumber(p, q); return 0; } |
Java
//Java implementation of the approach import java.io.*; class GFG { // Function to calculate gcd static int __gcd(int a, int b) { // Everything divides 0 if (a == 0 || b == 0) return 0; // base case if (a == b) return a; // a is greater if (a > b) return __gcd(a - b, b); return __gcd(a, b - a); } // Function to return the minimum valid number // that satisfies the given conditions static int minValidNumber(int p, int q) { // If possible if (q % p == 0) return __gcd(p, q); else return -1; } // Driver Code public static void main (String[] args) { int p = 2, q = 6; System.out.print(minValidNumber(p, q)); // THis code is contributed by Sachin. } } |
Python3
# Python3 implementation of the approach from math import gcd # Function to return the minimum # valid number that satisfies the # given conditions def minValidNumber(p, q) : # If possible if (q % p == 0) : return gcd(p, q) else : return -1 # Driver Code if __name__ == "__main__" : p, q = 2, 6; print(minValidNumber(p, q)) # This code is contributed by Ryuga |
C#
// C# implementation of the approach using System; class GFG { // Function to calculate gcd static int __gcd(int a, int b) { // Everything divides 0 if (a == 0 || b == 0) return 0; // base case if (a == b) return a; // a is greater if (a > b) return __gcd(a - b, b); return __gcd(a, b - a); } // Function to return the minimum valid number // that satisfies the given conditions static int minValidNumber(int p, int q) { // If possible if (q % p == 0) return __gcd(p, q); else return -1; } // Driver Code public static void Main() { int p = 2, q = 6; Console.Write(minValidNumber(p, q)); } } // THis code is contributed // by Mukul Singh |
PHP
<?php // Php implementation of the approach function gcd($a, $b) { // Everything divides 0 if($b == 0) return $a ; return gcd($b , $a % $b); } // Function to return the minimum valid // number that satisfies the given conditions function minValidNumber($p, $q) { // If possible if ($q % $p == 0) return gcd($p, $q); else return -1; } // Driver Code $p = 2; $q = 6; echo minValidNumber($p, $q); // This code is contributed by ita_c ?> |
2
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