Search for "small" solutions of a + b + c = abc = 6; see http://math.stackexchange.com/questions/1384653.

Question1384653.java

public class Question1384653 {
	final static Rational six = new Rational (6);
	
	public static void main (String [] args) {
		for (int suma = 2;;suma++) {
			System.out.println ("sum " + suma); 
			for (int pa = 1,qa = suma - 1;pa < suma;pa++,qa--)
				if (Rational.gcd (pa,qa) == 1)
					for (int signa = -1;signa <= 1;signa += 2) {
						Rational a = new Rational (signa * pa,qa);
						for (int sumb = 2;sumb <= suma;sumb++)
							for (int pb = 1,qb = sumb - 1;pb < sumb;pb++,qb--) {
								if (Rational.gcd (pb,qb) == 1)
									for (int signb = -1;signb <= 1;signb += 2) {
										Rational b = new Rational (signb * pb,qb);
										Rational c = six.subtract (a).subtract (b);
										if (a.multiply (b).multiply (c).equals (six))
											System.out.println (a + " " + b + " " + c);
									}
							}
					}
		}
	}
}