Find the other number when LCM and HCF given
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)
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