$\text{gcd}(a, b, c) = \text{gcd}(\text{gcd}(a, b), c)$

$\text{gcd}(a, b, c) = \text{gcd}(a, b) + \text{gcd}(b, c)$

$\text{gcd}(a, b, c) = \text{lcm}(a, b, c)$

$\text{gcd}(a, b, c) = \text{gcd}(a, b) \cdot \text{gcd}(b, c)$