Moderate# Consecutive Integers: What Must be True?

GMAT-SIK5SM

If $x$, $y$, and $z$ are a set of positive, consecutive integers where $x< y< z$, which of the following must be **TRUE**?

I. $x\times y$ is an even number

II. $y\times z$ is an even number

III. $x\times y\times z$ is an even number.