GCD at least 1

Theorem

The greatest common divisor is at least $1$:

$\forall a, b \in \Z^*: \gcd \left\{{a, b}\right\} \ge 1$

Proof

From One Divides All Integers:

$\forall a, b \in \Z^*: 1 \backslash a \land 1 \backslash b \implies 1 \le \gcd \left\{{a, b}\right\}$

$\blacksquare$