Brian the engineer disassembles an old Warcom press brake, and begins playing with the gears he finds inside it.
He has 3 cogs: A, B, and C. All of which have at least 8 teeth, and no cog has more than 40 teeth.
Cog B is the biggest and has the same number of teeth as cogs A and C added together.
Brian arranges the cogs as shown below. A red dot is drawn at the top of each of the cogs, and cog A has a crank handle attached to it, also shown in the diagram.
As the crank handle is turned, Brian notices the dots rotate out of their positions at different speeds.
He continues to turn the crank handle in the same direction until all three of the dots simultaneously appear back in the positions they started in, and then stops turning.
Brian reports that during the turning, cog C made 45 revolutions more than cog A.
How many teeth do each of the cogs have?
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