Mining information from a database is the main aim of data mining since years. The most relevant information which one requires as a result of data mining is getting associations between various attributes. More preciously mining frequent itemset is the most significant step to initiate the mining operation. Most of the algorithms discussed in the literature require multiple scan of the database to get the information on various sub steps of the algorithm which becomes quite computationally extensive. In this paper, we are proposing an algorithm Lexicographic Frequent Itemset Generation (LFIG), which can extract maximum information from a database only in one scan. We will use Lexicographic ordering of attributes and arrange itemsets in multiple hashes which are linked to their logical predecessor.