Given gcd(x,y)=g\text{gcd}(x, y) = ggcd(x,y)=g and lcm(x,y)=L\text{lcm}(x, y) = Llcm(x,y)=L, which of the following is true regarding the expression Lg\frac{L}{g}gL?
It is always a prime number.
It is always a perfect square.
It is equal to the product of the distinct prime factors of xxx and yyy that have differing exponents.
It is equal to xg×yg×g\frac{x}{g} \times \frac{y}{g} \times ggx×gy×g.