Given that 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, what is the relationship between gcd(a2,b2)\text{gcd}(a^2, b^2)gcd(a2,b2) and g2g^2g2?
gcd(a2,b2)=g2\text{gcd}(a^2, b^2) = g^2gcd(a2,b2)=g2
gcd(a2,b2)=L2\text{gcd}(a^2, b^2) = L^2gcd(a2,b2)=L2
gcd(a2,b2)=g⋅L\text{gcd}(a^2, b^2) = g \cdot Lgcd(a2,b2)=g⋅L
gcd(a2,b2)=(g⋅L)2\text{gcd}(a^2, b^2) = (g \cdot L)^2gcd(a2,b2)=(g⋅L)2