Given gcd(a,b)=g\text{gcd}(a, b) = ggcd(a,b)=g, which of these identities is correct for all positive integers a,ba, ba,b?
lcm(a,b)=a+bg\text{lcm}(a, b) = \frac{a+b}{g}lcm(a,b)=ga+b
gcd(a,b)⋅lcm(a,b)=a⋅b\text{gcd}(a, b) \cdot \text{lcm}(a, b) = a \cdot bgcd(a,b)⋅lcm(a,b)=a⋅b
gcd(a,b)=gcd(a,a+b)\text{gcd}(a, b) = \text{gcd}(a, a+b)gcd(a,b)=gcd(a,a+b)
lcm(a,b)=a⋅b⋅g\text{lcm}(a, b) = a \cdot b \cdot glcm(a,b)=a⋅b⋅g