Originally Posted by
humancongereel
just like 48x16, it's a 3:1 ratio. and 48x12 is a 4:1 ratio. i forget the proper mathematical term for expressing it, but the ratios can be reduced to an integer:1 ratio.
The number of skid patches is equal to the number of teeth on the cog divided by the greatest common factor between the chainring and cog.
Since 15 divides 45, the greatest common factor is 15 and you are left with one skid patch.
The best gear combinations are ones that are relatively prime - their greatest common factor is 1.