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If the bicycle has external gears (several visible sprockets that the chain can run over) then you get the number of "speeds" by multiplying the number of sprockets by the pedals with the number of sprockets at the rear wheel. Most common for a half-decent MTB would be 3x9 = 27 speeds.

In reality this isn't entirely true, some of those combos will give the same gear ratios, and some shouldn't be used due to the chain running at an extreme angle. So in practical terms a 27-speed bike will give something like 15-18 usefully different gears.

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