LiDAR point clouds are a rich source of information for autonomous vehicles and ADAS systems. However, they can be challenging to segment for moving objects as - among other things - finding correspondences between sparse point clouds of consecutive frames is difficult. Traditional methods rely on a (global or local) map of the environment, which can be demanding to acquire and maintain in real-world conditions and the presence of the moving objects themselves. This paper proposes a novel approach using as minimal sweeps as possible to decrease the computational burden and achieve mapless moving object segmentation (MOS) in LiDAR point clouds. Our approach is based on a multimodal learning model with single-modal inference. The model is trained on a dataset of LiDAR point clouds and related camera images. The model learns to associate features from the two modalities, allowing it to predict dynamic objects even in the absence of a map and the camera modality. We propose semantic information usage for multi-frame instance segmentation in order to enhance performance measures. We evaluate our approach to the SemanticKITTI and Apollo real-world autonomous driving datasets. Our results show that our approach can achieve state-of-the-art performance on moving object segmentation and utilize only a few (even one) LiDAR frames.