# Gearing

Gearing consists of two wheels, one is 88 and second 56 teeth. How many times turns smaller wheel to fit the same teeth as in the beginning? How many times will turn biggest wheel?

Result

n =  11
m =  7

#### Solution:

$88 = 2 \cdot 2 \cdot 2 \cdot 11 \ \\ 56 = 2 \cdot 2 \cdot 2 \cdot 7 \ \\ \ \\ \text{LCM}(88, 56) = 616 \ \\ n = 616/56 = 11$
$m = 616/88 = 7$

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