LCM of all the numbers in an array in Java

Question

I have an array of ints, and I'm trying to find the LCM (least common multiple) of all the values in the array. I've written an lcm method separately; it takes two values as input, and returns the lcm. My lcm method works perfectly fine, but when I use it to find the LCM of all the values I get a wrong answer.

Here are my gcd and lcm methods:

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


public static int lcm(int a, int b){
    return ((a*b)/gcd(a,b));

} 

This is what I have for the lcm of the array values:

public static int lcmofarray(int[] arr, int start, int end){
    if ((end-start)==1) return lcm(arr[start],arr[end-1]);
    else return (lcm (arr[start], lcmofarray(arr, start+1, end)));
}

When I put in an array that has the numbers 1 to 5 as arr, 0 as start and the length of the array as end, I get 30 as the answer, while I want 60. When I put in an array containing all the numbers from 1 to 10, I get 840 instead of 2520. I really can't explain that.

The algorithm should work--I've worked it out in my head. Can't figure out what the problem is with my code.

Any help will be appreciated.

Solution 1

If you change your gcd function to

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

it should work okay.

Solution 2

This is the program to find lcm and gcd for array of n numbers using formula lcmgcd=ab

public class Main
{
    public static void main(String[] args) {
        int a[]={63,105,210};
        int lcm=1,fir=lcm,res=0;
        for(int i=0;i<a.length;i++)
        {
            int sec=a[i];
            lcm=(fir*sec)/gcd(fir,sec);
            fir=lcm;
        }
        for(int j=0;j<a.length;j++)
        {
            res=gcd(res,a[j]);
        }
        System.out.println("lcm is "+lcm+" "+"gcd is "+res);
    }
    
    public static int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }
}