Question 1099504
<br>In any period of time, the number of teeth that mesh on the two gears must be the same.<br>
So the number of teeth that have to mesh for the two gears to get back to their original orientation is the least common multiple of the numbers of teeth on the two gears.<br>
The LCM of 10 and 12 is 60.<br>
The gear with 10 teeth will make 60/10 = 6 revolutions; and the gear with 12 teeth will make 60/12 = 5 revolutions.