The answer to this question really depends on your car. Most of the cars on the road today are front-wheel-drive, and a few are rear-wheel drive. These don't necessarily need to have all four tires replaced at once. Usually two at a time is sufficient. But all-wheel-drive systems are becoming more popular, and they do require all four tires to be replaced at one time. So for AWD vehicles, the short answer is yes, but let's find out why.
In vehicles with all-wheel-drive systems, including Subarus, Audis and Lamborghinis, the differential and the computer work together to send the right amount of torque to each wheel to minimize slippage and maximize control. If one of the tires is a different size than the others -- because three tires are worn and one is brand new -- the computer will take an incorrect reading and the differential will work too hard. Drive this way long enough and you'll burn out the drivetrain.
There are exceptions, even for AWD vehicles. If the tires only have a couple thousand miles on them and one needs to be replaced, that's okay according to Dominick Infante, National Manager of Product Communications for Subaru. Also, if you need to use the small spare to limp to the nearest repair shop, that's probably not far enough to do any serious damage.
Remember to rotate your tires because it extends their life on any vehicle; but for AWD vehicles, rotating the tires also makes sure that the tread wears evenly and doesn't place a strain on the drivetrain.
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