Given gcd(a,b)=g\text{gcd}(a, b) = ggcd(a,b)=g and lcm(a,b)=L\text{lcm}(a, b) = Llcm(a,b)=L, which of the following expressions is always equivalent to a+ba+ba+b?
g+Lg + Lg+L
g(k+Lg)g(k + \frac{L}{g})g(k+gL) for some integer kkk
gL\sqrt{gL}gL
gcd(a+b,L)\text{gcd}(a+b, L)gcd(a+b,L)