Neural networks can be used as associative memories which can learn problems of acquiring input-output relations presented by examples. The learning time problem addresses how long it takes for a neural network to learn a given problem by a learning algorithm. As a solvable model to this problem we analyze the learning dynamics of the linear associative memoty with the least-mean-square algorithm. Our result shows that the learning time τ of the linear associative memory diverges in τ (1-ρ)-2 as the memory rate ρ approaches 1. It also shows that the learning time exhibits the exponential dependence on ρ when ρ is small.