Greatest Common Divisor is at least 1

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Let $a, b \in \Z$ be integers.

The greatest common divisor of $a$ and $b$ is at least $1$:

$\forall a, b \in \Z_{\ne 0}: \gcd \set {a, b} \ge 1$


From One Divides all Integers:

$\forall a, b \in \Z: 1 \divides a \land 1 \divides b$

and so:

$1 \le \gcd \set {a, b}$

as required.