# Least common multiple between the number of poles and the number of slots

This value is the lowest number that is a multiple of both the number of poles and the number of slots. It is an indicator for what levels of cogging torque one can expect.

The least common multiple between the pole and slot numbers is a criteria for selecting the combination of poles and slot number. Choosing a number of poles and slots with a large least common multiple generally results in a low cogging torque. The cogging torque is the generally undesired torque at no-load conditions, i.e., at open circuit.

A safe way to get a large value of least common multiple (LCM) is to choose the number of slots close to the number of poles (only applicable to concentrated windings):
Examples: (from the Emetor winding calculator)
14-pole 6-slot concentrated winding: LCM = 42
14-pole 9-slot concentrated winding: LCM = 126
14-pole 12-slot concentrated winding: LCM = 84
14-pole 15-slot concentrated winding: LCM = 210
14-pole 18-slot concentrated winding: LCM = 126
14-pole 21-slot concentrated winding: LCM = 42
14-pole 24-slot concentrated winding: LCM = 168

Remark: The cogging torque depends also on other parameters such as the slot opening width, eventual magnet width, skewing, etc. Adjusting these parameters may reduce the cogging torque even if the combination of pole and slot numbers is not favorable. In addition, a low cogging torque does not always guarantee a low torque ripple at load conditions.