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Ryan Lochte and Kayla Reid both described their marriage as "irretrievably broken," TMZ Sports has learned.

According to court documents we obtained, when Reid filed for divorce from the Olympic great in late March, she stated the grounds for the split were "the marriage of the parties is irretrievably broken." In his answer to Reid's petition -- which was filed in late April -- Lochte wrote the same. Gallery Launch Gallery Getty/Instagram

Both agreed their date of marriage was Jan. 9, 2018 ... but the two differed on the actual date of their split. Reid called it March 7 ... while Lochte said it simply happened in April.

In her filing, Reid asked for alimony payments from Lochte -- though it's not clear how much exactly she's requesting ... especially

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