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One solution would be to change LinkedList to ArrayList and change the second loop that uses j variable to start from i as solutions 2 to i were already checked.

This solution improved execution time from 0.67 sec to 0.09 sec:

import java.util.LinkedList;
import java.util.ArrayList;

public class LinkedListEx {

    public static void main(String[] args) {
        
        long startTime = System.nanoTime();

        List<Integer> ll = new ArrayList<Integer>();
        for(int i = 2; i< 10000; i++)
        {
            ll.add(i);
        }
        
        int ls = ll.size();
        
        for(int i=2; i < ls/2; i++)
        {
           // start from i
            for(int j =i; j<ls/2; j++)
            {
                int x = i*j;
                if(x<ls)
                    ll.remove(new Integer(x));
            }
            
            int y = i*i;

            if(y<ls)
                ll.remove(new Integer(y));
        }
        
        long endTime = System.nanoTime();
        
        double timeTakenToExecuteInSeconds = (double)(endTime - startTime)/1_000_000_000.0;
        
        System.out.println(ll);
        System.out.println(timeTakenToExecuteInSeconds);

    }
}