A precise state estimate is crucial for a tight feedback control that enables agile and near-obstacle flights of UAVs. The state-of-the-art methods fuse slow pose measurements with high-frequency inertial measurements to obtain a precise state estimate. However, the inertial measurements from the IMU onboard the UAV are degraded by vibrations from spinning propellers and the precision of the estimated state suffers. We propose a novel approach based on the preintegration of accelerations obtained from motor speeds of individual propellers. We show that the accelerations obtained in this manner can be used for state propagation on their own to achieve better precision without including the IMU. Further, we propose a factor composed of the preintegrated motor speeds that can be directly employed in factor graph optimization frameworks. We combine our factor with LiDAR measurements into the proposed MAS-LO algorithm, which we open-source. Lastly, we evaluate estimation precision against a state-of-the-art inertial algorithm LIO-SAM to show a 28% improvement in position and 65% in velocity estimation accuracy, 14% lower measurement lag, and robustness to wrong parameter values.