can someone tell me what are the most common ratios for the T35 and T37 differentials ?

13,14,&15 x54

OK , 3 different . I will start to make some 54X14 , later the other ones . In case somebody needs a unusual ratio , let me know .

Can someone tell me if they made LSD versions in the factory ?

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https://t.me/pump_upp

If you listen to the UK racers they seem to be certain Molsheim used a LSD in the T51.
They needed that myth in order to justify its use for races under FIA jurisdiction.
However in the past 35 years nobody has been able to show me any evidence of a LSD being used by Bugatti in a T51 let alone T35.
Any insider will confirm that with or without LSD at Monaco is an unequal fight.
In short: If Bugatti made/used LSD's it was just before but more likely after WW2 .
Bugwrench

What kind of LSD did Bugatti use ? Can you show a foto ?

After reading my post you should not ask me that question......
Today the ZF type cam and pawl is (illegally) used by many.
Bugwrench

I think you are quite right.It is interesting [to me at least ! ] that my T252 rear axle has a ZF diff as original but not limslip just normal.The T251 used ZF gears and syncros,bought off the shelf.I have spoken to the still living Bugatti worker who went to get them from ZF. Had Bugatti lost the art of making gears by 1954? Or was it cheaper?