The present disclosure relates to methods for producing human milk oligosaccharide (HMO) core structures using glycosidases from family GH20 hexosaminidases. In particular, the present disclosure provides methods for producing lacto-N-triose II (LNT II) and/or lacto-N-tetraose (LNT) by reacting glucosamine-oxazoline and/or lacto-N-biose-oxazoline with lactose catalysed by an enzyme of the glycoside hydrolase family 20 (GH20) according to the classification of the Carbohydrate-Active-Enzymes (CAZy) database. Specific optimized enzymes are identified to catalyse the reactions.