How to determine the LCM of an array of numbers?

This solution exploits two properties of LCM: i) LCM(a,b) = (a.b)/GCD(a, b) and LCM(a, b, c) = LCM(a, LCM(a,b)).

package personal.puzzles;

public class LCMEuclid {

    public int findLCMOfArray(int[] array) {
        if (array.length == 0) {
            throw new IllegalArgumentException("You cannot determine LCM of empty array");
        } else if (array.length == 1) {
                return array[0];
        }
        int first = array[0];
        int second = array[1];
        int lcm = findLCMOfPair(first, second);
        for (int i = 2; i < array.length; ++i) {
            lcm = findLCMOfPair(lcm, array[i]);
        }
        return lcm;
    }
    
    private int findLCMOfPair(int first, int second) {
        return first * second / gcd(first, second);
    }
    
    private int gcd(int first, int second) {
        while (first % second != 0) {
            int tempSecond = first % second;
            first = second;
            second = tempSecond;
        }
        return second;
    }
    
    public static void main(String[] args) {
        int a[] = {21, 6, 7, 11};
        LCMEuclid lcmEuclid = new LCMEuclid();
        System.out.println(lcmEuclid.findLCMOfArray(a));
    }
}