Find the other number when LCM and HCF given

Given a number A and L.C.M and H.C.F. The task is to determine the other number B.

Examples:

Input: A = 10, Lcm = 10, Hcf = 50.
Output: B = 50

Input: A = 5, Lcm = 25, Hcf = 4.
Output: B = 20

Formula:

A * B = LCM * HCF 
B = (LCM * HCF)/A
Example : A = 15, B = 12 
HCF = 3, LCM = 60 
We can see that 3 * 60 = 15 * 12.

How does this formula work?
Since HCF divides both the numbers, let. 
A = HCF * x 
B = HCF * y
Note that x and y are not common factors, so LCM must include HCF, x and y. 
So we can conclude. 
LCM = HCF * x * y
So LCM * HCF = HCF * x * y * HCF which is equal to A * B

Below is the implementation of the above approach: 

C++

// CPP program to find other number from given
// HCF and LCM
#include <bits/stdc++.h>
using namespace std;

// Function that will calculates
// the zeroes at the end
int otherNumber(int A, int Lcm, int Hcf)
{
    return (Lcm * Hcf) / A;
}

// Driver code
int main()
{
    int A = 8, Lcm = 8, Hcf = 1;

    // Calling function.
    int result = otherNumber(A, Lcm, Hcf);

    cout << "B = " << result;

    return 0;
}

Java

// Java program to find other number from given
// HCF and LCM
import java.io.*;

class GFG{

// Function that will calculates
// the zeroes at the end
static int otherNumber(int A, int Lcm, int Hcf)
{
    return (Lcm * Hcf) / A;
}

// Driver code
public static void main(String args[])
{
    int A = 8, Lcm = 8, Hcf = 1;

    // Calling function.
    int result = otherNumber(A, Lcm, Hcf);

    System.out.println("B = "+ result);

}
}

Python3

# Python 3 program to find other
# number from given HCF and LCM

# Function that will calculates
# the zeroes at the end
def otherNumber(a, Lcm, Hcf):
    return (Lcm * Hcf) // A

# Driver code
A = 8; Lcm = 8; Hcf = 1

# Calling function
result = otherNumber(A, Lcm, Hcf)
print("B =", result)

# This code is contributed
# by Shrikant13

C#

// C# program to find other number
// from given HCF and LCM
using System;

class GFG
{

// Function that will calculates
// the zeroes at the end
static int otherNumber(int A, int Lcm,
                              int Hcf)
{
    return (Lcm * Hcf) / A;
}

// Driver code
static public void Main(String []args)
{
    int A = 8, Lcm = 8, Hcf = 1;

    // Calling function.
    int result = otherNumber(A, Lcm, Hcf);

    Console.WriteLine("B = " + result);
}
}

// This code is contributed by Arnab Kundu

PHP

<?php
// PHP program to find other number
// from given HCF and LCM

// Function that will calculates
// the zeroes at the end
function otherNumber($A, $Lcm, $Hcf)
{
    return ($Lcm * $Hcf) / $A;
}

// Driver code
$A = 8; $Lcm = 8; $Hcf = 1;

// Calling function.
$result = otherNumber($A, $Lcm, $Hcf);

echo "B = " . $result;

// This code is contributed
// by Akanksha Rai

Javascript

<script>

// Javascript program to find other number from given
// HCF and LCM

// Function that will calculates
// the zeroes at the end
function otherNumber(A, Lcm, Hcf)
{
    return (Lcm * Hcf) / A;
}

// Driver code

    let A = 8, Lcm = 8, Hcf = 1;

    // Calling function.
    let result = otherNumber(A, Lcm, Hcf);

    document.write("B = " + result);

// This code is contributed by Mayank Tyagi

</script>

Output

B = 1

Time Complexity: O(1)
Auxiliary Space: O(1)