Max tire size for 2500

Got a 2004 2500HD, Diesel, Alison, 4wd and looking to put the maximum size tire on the stock rims. Something with a fairly agressive tread pattern for dirt.
What's the max size I can go with and can I get a correction on my speedometer/odometer?
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I'm running 285/75R16 on my '02. I'm told that's the biggest you can run. Don't know about speedo corrections.

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