If GCD(a,b)=g\text{GCD}(a, b) = gGCD(a,b)=g, what is GCD(a+kb,b)\text{GCD}(a+kb, b)GCD(a+kb,b)?
ggg
kgkgkg
g+kg+kg+k
GCD(a,kg)\text{GCD}(a, kg)GCD(a,kg)