What is the minimum number of rotations Gear 1 requires to return to this starting position?

Question

Two gears are shown below in their starting position.
Gear 1 has 6 teeth
Gear 2 has 8 teeth
As Gear 1 turns, it cause Gear 2 to turn at a different rate
Gear 1 is rotated until the two gears are back to this starting position??
What is the minimum number of rotations Gear 1 requires to return to this starting position?

A. 48 rotations
B. 24 rotations
C. 4 rotations
D. 2 rotations

I know the answer is C, but I chose D and I do not get how to get that number...
Thanks

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Answer 1 · 2017-11-11T11:25:32

We can figure this out by finding the LCF.

gear 1 will be $S$ $S$

gear 2 will be $L$ $L$

.

$S = 6, 12, 18, 24$ $S = 6, 12, 18, color(red)24$ -

$L = 8, 16, 24$ $L = 8, 16, color(red)24$ -

factors that make up $24$ $24$ are $6 \cdot 4$ $6*4$ and $8 \cdot 3$ $8*3$

we can remove $8 \cdot 3$ $8*3$ because neither gear has odd teeth and $8$ $8$ is not a factor in $S$ $S$

$6$ $6$ does not show up in $L$ $L$ so we are left with the only choice which is as you mentioned the correct answer $4$ $4$