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 endint otherNumber(int A, int Lcm, int Hcf){ return (Lcm * Hcf) / A;}// Driver codeint 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 codeA = 8; Lcm = 8; Hcf = 1# Calling functionresult = 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 endfunction 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)
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