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++

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// 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;
}

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Java

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// Java program to find other number from given 
// HCF and LCM 
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); 
  
}

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Python3

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# 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

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C#

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// 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

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PHP

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<?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

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Output:

B = 1


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