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Many new narrowband low-power wide-area networks (LPWANs) (e.g., LoRaWAN, Sigfox) have opted to use pure ALOHA-like access for its reduced control overhead and asynchronous transmissions. Although asynchronous access reduces the energy consumption of IoT devices, the network performance suffers from high intra-network interference in dense deployments. Contrarily, synchronous access can improve throughput and fairness, but it requires time synchronization. Unfortunately, maintaining synchronization over the narrowband LPWANs wastes channel time and transmission opportunities. In this paper, we propose the use of out-of-band time-dissemination to relatively synchronize LoRa devices and thereby facilitate resource-efficient slotted uplink communication. To this end, we conceptualize and analyze a co-designed synchronization and random access mechanism that can effectively exploit technologies providing limited time accuracy, such as FM radio data system (FM-RDS). While considering the LoRa-specific parameters, we derive the throughput of the proposed mechanism, compare it to a generic synchronous random access using in-band synchronization, and design the communication parameters under time uncertainty. We scrutinize the transmission time uncertainty of a device by introducing a clock error model that accounts for the errors in the synchronization source, local clock, propagation delay, and transceiver's transmission time uncertainty. We characterize the time uncertainty of FM-RDS with hardware measurements and perform simulations to evaluate the proposed solution. The results, presented in terms of success probability, throughput, and fairness for a single-cell scenario, suggest that FM-RDS, despite its poor absolute synchronization, can be used effectively to realize slotted LoRa communication with performance similar to that of more accurate time-dissemination technologies.