lcd.java

public class lcd {
    public static void main(String[] args) {
        int x = 6;
        int y = 23;
        int a = 7;
        int b = 3;
        System.out.println("Single method LCD: "+leastCommonDenominatorsngl(x, y, a , b));
        System.out.println("LCD ethod w/ GCD helper: "+leastCommonDenominatordbl(x, y, a, b));
        System.out.println("For loop method LCD: "+leastCommonDenominatorLoop(x, y, a, b));

    }

    //Least common denominator method with recursion. Does not call any helper methods. I dislike this implementation 
    //because it is less clear what the code is actually doing.
    //In order to make this method work as a single method I used the x variable as a flag so that on the last method call on the stack I can do
    //the math to calculate LCD and in all other method calls above it in the stack I just return the GCD. 
    public static int leastCommonDenominatorsngl(int x, int y, int a, int b) {
        if( y ==0){
            return b;
        }
        int gcd = leastCommonDenominatorsngl(-Math.abs(x), b%y, a, y); //x is passed as negative as a flag so that the method returns the GCD
        if( x<0){
            return gcd;
        }
        else{           //in the last call on the stack x is positive and the gcd is use to calculate the LCD, can easily fail if user passes negative x values
        return (y*b)/gcd;}
    }

    //Least common denominator method with recursion. in this case the recursive method in the gcd() method being called as a helper method
    //I prefer this implementation because the code is much simpler and easy to read.
    public static int leastCommonDenominatordbl(int x, int y, int a, int b){
        int gcd = gcd(y, b);
        return (y*b)/gcd;
    }
    public static int gcd(int a,int b){
        if(a == 0){
            return b;
        }
        return gcd(b%a,a);
    }

    //LCD without recursion 
    public static int leastCommonDenominatorLoop(int x, int y, int a, int b){
        int gcdA = y;
        int gcdB = b;
        while(!(gcdA==0)){
            int temp = gcdA;
            gcdA = gcdB%gcdA; 
            gcdB= temp;
        }
        return (y*b)/gcdB;
    }
}