Fraction shenanigans

Lcm.java

	/** Returns the greatest common divisor (factor) of positive integers a and b
	 * <p>Source: https://en.wikipedia.org/wiki/Binary_GCD_algorithm
	 */
	private static int gcdUnsigned(int u, int v) {
		// simple cases (termination)
		if (u == v) return u;
		if (u == 0) return v;
		if (v == 0) return u;

		// look for factors of 2
		if ((u&1)==0) { // u is even
			if ((v&1)==1) { // v is odd
				return gcdUnsigned(u >> 1, v);
			} else { // both u and v are even
				return gcdUnsigned(u >> 1, v >> 1) << 1;
			}
		}
		if ((v&1)==0) {// u is odd, v is even
			return gcdUnsigned(u, v >> 1);
		}
		// reduce larger argument
		if (u > v)
			return gcdUnsigned((u - v) >> 1, v);

		return gcdUnsigned((v - u) >> 1, u);
	}
	
	/** Handles the one additional case for fractions which potentially have -1 as a factor */
	public static int gcd(int a, int b) {
		int gcd = gcdUnsigned(Math.abs(a), Math.abs(b));
		if (a<0 && b<0) { //-1 is also a common factor
			return -gcd;
		} else {
			return gcd;
		}
	}
	
	/**
	 * Returns the least common multiple of integer divisors a and b
	 * <p>Source: https://en.wikipedia.org/wiki/Least_common_multiple#Using_the_greatest_common_divisor
	 */
	public static int lcm(int a, int b) {
		return Math.abs(a*b) / gcd(a, b);
	}