a lactic acid based by - product formed in a process of producing a lactic acid based composition is subjected to racemization in the presence or absence of a catalyst to thereby obtain a lactic acid component having substantially optical inactivity . then , lactide or polylactic acid having optical inactivity can be obtained from the lactic acid component having the optical inactivity . the obtained lactide or polylactic acid is mixed with lactide or polylactic acid having an optical purity in a range of 90 to 100 % e . e . at a predetermined ratio to thereby obtain lactide or polylactic acid having a desired optical purity .