The Least Cost Method is an approach used to find an initial basic feasible solution for transportation problems by prioritizing allocations based on the lowest transportation costs. In this method, the algorithm begins by examining the cost matrix, identifying the cell with the minimum cost, and allocating as much as possible to that cell without exceeding the supply and demand constraints. Once an allocation is made, the corresponding row or column is adjusted (or eliminated) based on whether the supply or demand has been fully satisfied, and the process continues by repeating the search for the next minimum cost cell until all supplies and demands are fulfilled. This method often leads to a more cost-effective initial solution compared to other methods, such as the Northwest Corner Rule.