# Gears

The gearing fits wheel with 20 teeth to the wheel with 36 teeth. Before starting the machine is stained tooth smaller wheels in the designated space between the teeth of the larger wheels. How many times after starting the machine wheels turning that stained teeth again fits into the designated spaces?

Correct result:

n1 =  9
n2 =  5

#### Solution:

$20=2^2 \cdot 5 \ \\ 36=2^2 \cdot 3^2 \ \\ LCM(20, 36)=2^2 \cdot 3^2 \cdot 5=180 \ \\ \ \\ a=LCM(20,36)=180 \ \\ n_{1}=a/20=180/20=9$
$n_{2}=a/36=180/36=5$

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