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#java #mathematics #lecture #gfg #geeksforgeeks #efficientmethod #naivemethod #euclidean #optimisedeuclidean #lcm

// Efficient Solution : Time Complexity : O(log(min(a,b)))
// a * b = gcd(a,b) * lcm(a,b)

import java.io.*;
import java.util.*;

public class Main {
	
	static int gcd(int a, int b)
	{
		if(b==0)
			return a;

		return gcd(b, a % b);
	}

	static int lcm(int a, int b)
	{
		return (a * b) / gcd(a, b); // constant no. of operations
	}
	
	public static void main (String[] args) {
		
		int a = 4, b = 6;

		System.out.println(lcm(a, b));

	}
}

// Naive Method : Time Complexity : O(a*b-max(a,b))


	static int lcm(int a, int b)
	{
		int res = Math.max(a,b);
		
		while(res > 0)
		{
		    if(res%a == 0 && res%b == 0)
		    {
		        return res;
		    }
		    res++;
		}
		return res;
	}

#java #mathematics #lecture #gfg #geeksforgeeks #efficientmethod #naivemethod #euclidean #optimisedeuclidean #gcd #hcf

GCD or HCF of two Numbers

// Optimised Euclidean Algorithm Code : Time Complexity : O(log(min(a,b)))

import java.io.*;
import java.util.*;

public class Main {

	static int gcd(int a, int b)
	{
		if(b==0)
			return a;

		return gcd(b, a % b);
	}

	public static void main (String[] args) {
		
		int a = 12, b = 15;

		System.out.println(gcd(a, b));

	}
}

// Euclidean Algorithm Code

  static int gcd(int a, int b)
  {
    while(a!=b)
    {
      if(a > b)
        a = a - b;
      else
        b = b - a; 
    }

    return a;
  }

// Naive Method : Time Complexity : O(min(a,b))

  static int gcd(int a, int b)
  {
    int res = Math.min(a,b);

    while(res > 0)
    {
      if(a%res == 0 && b%res == 0)
      {
        break;
      }
      res--;
    }

    return res;
  }

LCM of Two Numbers

GCD or HCF of two Numbers

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