Changing Gears

When a person pushes on the pedals of a bicycle, the pedals turn the front gear, the front gear pushes on the chain, the chain turns the back gear and the back gear turns the rear wheel.

In some cycles, it is possible to change the diameters of the front gear as well as the back gear. The cyclist can adjust the sizes of the gears to change the amount of force required to pedal.

A cyclist, who is riding uphill, wants to minimize the amount of force required. Which combination of gears will require the least force?

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