Question

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

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

Answer 1

We can figure this out by finding the LCF.

Explanation:

gear 1 will be `S`

gear 2 will be `L`

.

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

• gear 1 turn rotations.
  gear 1 moves in a rotation of 6

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

• gear 2 turn rotations
  gear 2 moves in a rotation of 8

factors that make up `24` are `6*4` and `8*3`

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

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