Which property is equivalent to the Euclidean algorithm step gcd(a,b)=gcd(b,a(modb))\text{gcd}(a, b) = \text{gcd}(b, a \pmod b)gcd(a,b)=gcd(b,a(modb))?
a=qb+r ⟹ gcd(a,b)=gcd(b,r)a = qb + r \implies \text{gcd}(a, b) = \text{gcd}(b, r)a=qb+r⟹gcd(a,b)=gcd(b,r)
gcd(a,b)=ablcm(a,b)\text{gcd}(a, b) = \frac{ab}{\text{lcm}(a, b)}gcd(a,b)=lcm(a,b)ab
a+b=gcd(a,b)+lcm(a,b)a+b = \text{gcd}(a, b) + \text{lcm}(a, b)a+b=gcd(a,b)+lcm(a,b)
gcd(a,b)=gcd(a−b,b)\text{gcd}(a, b) = \text{gcd}(a-b, b)gcd(a,b)=gcd(a−b,b)