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Lamar Odom -- Files Divorce Docs ... Umm, Exactly What She Said

Lamar Odom just filed his response to Khloe Kardashian's divorce petition ... and it shows the exes are lock step when it comes to this break up.

In the docs, obtained by TMZ Sports, Lamar lists the exact same date of separation as Khloe did -- December 13, 2013. Ditto for court's ability to award spousal support to the other. As we reported, our sources say they have a prenup.

They even agree each will pay for their own attorneys, a rarity in Hollywood divorces.

Now that Lamar's officially responded .