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

1 Answer
Nov 11, 2017

Answer:

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#