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How To Calculate Gcf In Addition To Lcm Of 2 Numbers Inwards Java? Example

This week's programming exercise is to write a Java plan to calculate GCF in addition to LCM of 2 numbers. The GCF, stands for Greatest mutual element in addition to LCM stands for Lowest mutual multiplier, both are pop mathematical functioning in addition to related to each other. The GCF is the largest expose which divides both the expose without leaving whatsoever residual e.g. if 2 numbers are 24 in addition to xl in addition to so their GCF is 8 because 8 is the largest expose which divides both 24 in addition to xl perfectly, without leaving whatsoever remainder. Similarly, LCM is the lowest expose which is perfectly divisible past times the 2 number, for example, if given expose is xl in addition to 24 in addition to so their LCM is 120 because this is the lowest expose which is perfectly divisible past times both xl in addition to 24.

Since, y'all tin calculate LCM 1 time y'all accept GCF because LCM of 2 numbers a in addition to b is goose egg but a*b/GCF(a, b). So, inward reality, nosotros simply take away to calculate the greatest mutual divisor start in addition to and so nosotros tin discover the lowest mutual multiplier.

One of the easiest means to discover GCF of 2 numbers is past times using Euclid's algorithm. This is a recursive algorithm which finds GCD of 2 numbers past times a radical reduction inward work size past times changing GCD(A, B) to GCD(B, H5N1 modernistic B)  where A>B.  The algorithm was proposed past times Euclid most 2250 years ago. See Introduction to Algorithms to larn to a greater extent than most the Euclidian  algorithm, an efficient means to discover the GCD of 2 numbers.

Anyway, It industrial plant similar below:

public static int GCF(int a, int b) {     if (b == 0) {       return a;     } else {       return (GCF(b, a % b));     }   }

You tin encounter that the base of operations illustration is when the minute expose overstep away zero, inward that case, GCF is goose egg but the start number, otherwise, it keeps calling GCF() method using recursion but every fourth dimension the minute expose overstep away smaller due to the role of modulus operator.

How does Euclid's algorithm calculate GCD

The Euclidean algorithm is slowly to sympathise 1 time y'all walk through the algorithm alongside an illustration in addition to encounter the flowchart. Let's calculate GCD of xl in addition to 24 using the Euclidean algorithm, scream back the start expose should hold out greater than minute inward enterprise to hold out used alongside this algorithm.

The start measurement is to cheque if the minute expose is zero, inward that illustration patently GCD is the start number. If that's non the illustration in addition to so the minute expose becomes the start in addition to a modernistic b becomes the minute expose e.g. forthwith nosotros take away to calculate GCD of 24 in addition to xl % 24 which is xvi i.e. GCD (24, 16) so our work is forthwith reduced.

Since the minute expose is however non zero, nosotros motility to the minute measurement over again in addition to this time, the algorithm calculates GCD(16, 8) because 24 % xvi = 8. Since 8 is however non equal to zero, nosotros over again motility to side past times side measurement in addition to this time, the algorithm calculates GCD(8, 0) because xvi modernistic 8 = zero. Now, the minute expose is null so the start expose is equal to GCD.

So, finally, the GCD of xl in addition to 24 is equal to 8 which is right because it is the largest expose which fully divides both xl in addition to 24.

Here is roughly other illustration of Euclidean algorithm to calculate greatest mutual divisor or greatest mutual factor:

You tin encounter that how measurement past times measurement work is reduced into calculating GCF of smaller numbers.

Java Program to calculate LCM in addition to GCF of 2 numbers

Here is our sample Java plan which finds the lowest mutual to a greater extent than multiple in addition to a greatest mutual divisor of 2 numbers using Euclid's method. This plan start calculates GCD or GCF using Euclidean Algorithm in addition to and so uses that method to calculate the LCM or lowest mutual multiplier.

If y'all desire to larn to a greater extent than most essential programming algorithms, I suggest y'all read a skilful majority on information structures in addition to algorithms e.g. Introduction to Algorithms past times Thomas H. Cormen, which explains primal mathematical in addition to programming algorithms inward elementary words.

Calculating LCM in addition to GCD of 2 numbers inward Java

public class LCM {    public static void main(String[] args) {     System.out.println("Welcome to Java Program to calculate LCM in addition to GCF of 2 numbers");     Scanner sc = new Scanner(System.in);      System.out.println("Enter start number: ");     int n1 = sc.nextInt();     System.out.println("Enter minute number: ");     int n2 = sc.nextInt();      int gcf = GCF(n1, n2);     int lcm = LCM(n1, n2);      System.out.println("The Greatest mutual divisor (GCF) of 2 numbers are: "         + gcf);     System.out         .println("The Lowest mutual multiplier (LCM) of 2 numbers are: "             + lcm);      sc.close();   }    /**    * Java method to calculate lowest mutual multiplier of 2 numbers    *     * @param a    * @param b    * @return LCM of 2 numbers    */   public static int LCM(int a, int b) {     return (a * b) / GCF(a, b);   }    /**    * Java method to calculate greatest mutual element of 2 numbers    *     * @param a    * @param b    * @return GCF of 2 numbers using Euclid's algorithm    */   public static int GCF(int a, int b) {     if (b == 0) {       return a;     } else {       return (GCF(b, a % b));     }   }  }  Output Welcome to Java Program to calculate LCM and GCF of 2 numbers Enter first number:  xl Enter minute number:  24 The Greatest mutual divisor (GCF) of 2 numbers are: 8 The Lowest mutual multiplier (LCM) of 2 numbers are: 120  Welcome to Java Program to calculate LCM and GCF of 2 numbers Enter first number:  nine Enter minute number:  342 The Greatest mutual divisor (GCF) of 2 numbers are: nine The Lowest mutual multiplier (LCM) of 2 numbers are: 342

That's all most how to discover the GCF in addition to LCM of 2 numbers inward Java. It's rattling slowly to produce alongside Euclid's algorithm because 1 time y'all accept GCF, calculating LCM is goose egg but a*b/GCF(a,b). If y'all desire roughly to a greater extent than Java programs similar this to do in addition to amend your coding feel in addition to programming logic, cheque out the next listing of programs from interviews.

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