Simple Algorithms- Fibonacci,finding GCD & finding LCM

Algorithm 1- Finding Fibonacci number with better time complexity

import java.util.Scanner;

//0,1,1,2,3,5,8,13,21,34...

//fun(n)=fun(n-1)+fun(n-2) where n>=2

/*fib(9)=fib(8)+fib(7)

=fib(7)+fib(6)+fib(6)+fib(5)

=fib(6)+fib(5)+fib(5)+fib(4)+fib(5)+fib(4)+fib(4)+fib(3)

*/

public class FibonacciNumberFast {

     public static void main(String[] args) {

           Scanner scanner = new Scanner(System.in);

           int n = scanner.nextInt();

           long fno=fibonacciNumber(n);

           System.out.println(fno);  

     }

     public  static long fibonacciNumber(int n){

           int array[]= new int[n+1];

           array[0]=0;

           if(n==0)

                return array[0];

           array[1]=1;

           for(int i=2;i<=n;i++)

                array[i]=array[i-1]+array[i-2];

           return array[n];

     }

}

Algorithm 2– Finding GCD of a number

 1) GCD using Recursion

                          2) GCD using naïve approach

import java.util.Scanner;

// Largest number which divides both a and b

public class GCDNaive {

     public static void main(String[] args) {

           Scanner scanner = new Scanner(System.in);

           long a = scanner.nextLong();

           long b = scanner.nextLong();

           //long gcd = gcd(a, b);

           //System.out.println("Result from GCD Naive "+gcd);

           gcdFast(a, b);

     }

     static void gcdFast(long a, long b) {

           if (b == 0) {

                System.out.println(a);

           System.exit(0);

           }

           long rem=a%b;

           gcdFast(b, rem);

     }

/*   static long gcd(long a, long b) {

           long best = 0;

           for (long i = 1; i <= a + b; i++) {

                if ((a%i ==0) && (b%i== 0))

                     best = i;

           }

           return best;

     }

*/}

Algorithm 3– Finding LCM of a number

import java.util.Scanner;

// GCD(a,b)*LCM(a,b)=a*b

public class LCM {

     public static void main(String[] args) {

           Scanner scanner = new Scanner(System.in);

           long a = scanner.nextLong(); // 8

           long b = scanner.nextLong(); // 6

           // long c = gcd(a, b);

           // System.out.println("GCD is" + c);

           long c = gcdFast(a, b);

           long d = (a * b) / c;

           System.out.println(d);

     }

     static long gcdFast(long a, long b) {

           if (b == 0) {

                return a;

           }

           long rem = a % b;

           long c=gcdFast(b, rem);

           return c;

     }

     /*   static long gcd(long a, long b) {

           long best = 0;

           for (long i = 1; i <= a + b; i++) {

                if ((a % i == 0) && (b % i == 0))

                     best = i;

           }

           return best;

     }*/

}