When incorporating machine-to-machine (M2M) communications into the Third-Generation Partnership Project (3GPP) Long-Term Evolution (LTE) networks, one of the challenges is the traffic overload since many machine-type communication (MTC) devices activated in a short period of time may require access to an evolved node B (eNodeB) simultaneously. One approach to tackle this problem is by using an access class barring (ACB) mechanism with an ACB factor to defer some activated MTC devices transmitting their access requests. In this paper, we first present an analytical model to determine the expected total service time, i.e., the time used by all MTC devices to successfully access the eNodeB. In the ideal case that the eNodeB is aware of the number of backlogged MTC devices, we determine the optimal value of the ACB factor to reduce traffic overload. To better utilize the random access resources shared among human users and MTC devices in LTE networks, we propose to dynamically allocate a number of random access preambles for MTC devices. We further propose two dynamic ACB (D-ACB) algorithms for fixed and dynamic preamble allocation schemes to determine the ACB factors without a priori knowledge of the system backlog. Simulation results show that the proposed D-ACB algorithms achieve almost the same performance as the optimal performance obtained in the ideal case. The proposed D-ACB for dynamic preamble allocation algorithm can reduce both the total time to serve all MTC devices and the average number of random access opportunities required by each MTC device.