: For a transaction database, a frequent itemset is an itemset included in at least a specified number of transactions. A frequent itemset P is maximal if P is included in no other frequent itemset, and closed if P is included in no other itemset included in the exactly same transactions as P. The problems of finding these frequent itemsets are fundamental in data mining, and from the applications, fast implementations for solving the problems are needed. In this paper, we propose efficient algorithms LCM (Linear time Closed itemset Miner), LCMfreq and LCMmax for these problems. We show the efficiency of our algorithms by computational experiments compared with existing algorithms.