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Find two numbers with the given LCM and minimum possible difference
  • Last Updated : 24 Jun, 2020
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Given an integer X, the task is to find two integers A and B such that LCM(A, B) = X and the difference between the A and B is minimum possible.

Examples:

Input: X = 6
Output: 2 3
LCM(2, 3) = 6 and (3 – 2) = 1
which is the minimum possible.

Input X = 7
Output: 1 7

Approach: An approach to solve this problem is to find all the factors of the given number using the approach discussed in this article and then find the pair (A, B) that satisfies the given conditions and has the minimum possible difference.



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 LCM of a and b
int lcm(int a, int b)
{
    return (a / __gcd(a, b) * b);
}
  
// Function to find and print the two numbers
void findNums(int x)
{
  
    int ans;
  
    // To find the factors
    for (int i = 1; i <= sqrt(x); i++) {
  
        // To check if i is a factor of x and
        // the minimum possible number
        // satisfying the given conditions
        if (x % i == 0 && lcm(i, x / i) == x) {
  
            ans = i;
        }
    }
    cout << ans << " " << (x / ans);
}
  
// Driver code
int main()
{
    int x = 12;
  
    findNums(x);
  
    return 0;
}

Java




// Java implementation of the approach
class GFG
{
  
    // Function to return the LCM of a and b
    static int lcm(int a, int b)
    {
        return (a / __gcd(a, b) * b);
    }
  
    static int __gcd(int a, int b) 
    {
        return b == 0 ? a : __gcd(b, a % b);
    }
  
    // Function to find and print the two numbers
    static void findNums(int x)
    {
  
        int ans = -1;
  
        // To find the factors
        for (int i = 1; i <= Math.sqrt(x); i++)
        {
  
            // To check if i is a factor of x and
            // the minimum possible number
            // satisfying the given conditions
            if (x % i == 0 && lcm(i, x / i) == x)
            {
  
                ans = i;
            }
        }
        System.out.print(ans + " " + (x / ans));
    }
  
    // Driver code
    public static void main(String[] args) 
    {
        int x = 12;
  
        findNums(x);
    }
}
  
// This code is contributed by 29AjayKumar

Python3




# Python3 implementation of the approach
from math import gcd as __gcd, sqrt, ceil
  
# Function to return the LCM of a and b
def lcm(a, b):
    return (a // __gcd(a, b) * b)
  
# Function to find and print the two numbers
def findNums(x):
  
    ans = 0
  
    # To find the factors
    for i in range(1, ceil(sqrt(x))):
  
        # To check if i is a factor of x and
        # the minimum possible number
        # satisfying the given conditions
        if (x % i == 0 and lcm(i, x // i) == x):
  
            ans = i
  
    print(ans, (x//ans))
  
# Driver code
x = 12
  
findNums(x)
  
# This code is contributed by mohit kumar 29

C#




// C# implementation of the approach
using System;
  
class GFG
{
  
    // Function to return the LCM of a and b
    static int lcm(int a, int b)
    {
        return (a / __gcd(a, b) * b);
    }
  
    static int __gcd(int a, int b) 
    {
        return b == 0 ? a : __gcd(b, a % b);
    }
  
    // Function to find and print the two numbers
    static void findNums(int x)
    {
  
        int ans = -1;
  
        // To find the factors
        for (int i = 1; i <= Math.Sqrt(x); i++)
        {
  
            // To check if i is a factor of x and
            // the minimum possible number
            // satisfying the given conditions
            if (x % i == 0 && lcm(i, x / i) == x)
            {
  
                ans = i;
            }
        }
        Console.Write(ans + " " + (x / ans));
    }
  
    // Driver code
    public static void Main(String[] args) 
    {
        int x = 12;
  
        findNums(x);
    }
}
  
// This code is contributed by 29AjayKumar
Output:
3 4

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