Presumably the desired condition is that gcd(n,m) = 1 (the number of teeth be relatively prime) so that each tooth of one gear meets with each tooth of the seco

Presumably the desired condition is that gcd(n,m) = 1 (the number of teeth be relatively prime) so that each tooth of one gear meets with each tooth of the second gear, cyclically. If there are variations/defects in teeth, this might help them wear more uniformly.