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Synchronized motion and pattern formation of magnetic particle aggregates in variable magnetic field is of growing interest from the point of view of both fundamental science and its applications. In this article, the role of size differences in synchronized motion of magnetic particles under external rotating magnetic field at low Reynolds number flow regimes is considered. Several different motion regimes are observed in simulations as a function of particle size differences and field rotation rate. Simulation indicates phase-like transitions between different motion regimes when particle size differences become significant. It is also shown that particle size differences permit the possibility of locomotion for particle aggregates which cannot be observed for uniform particle sizes.