Large Language Models (LLMs) for Recommendation (LLM4Rec) is a promising research direction that has demonstrated exceptional performance in this field. However, its inability to capture real-time user preferences greatly limits the practical application of LLM4Rec because (i) LLMs are costly to train and infer frequently, and (ii) LLMs struggle to access real-time data (its large number of parameters poses an obstacle to deployment on devices). Fortunately, small recommendation models (SRMs) can effectively supplement these shortcomings of LLM4Rec diagrams by consuming minimal resources for frequent training and inference, and by conveniently accessing real-time data on devices. In light of this, we designed the Device-Cloud LLM-SRM Collaborative Recommendation Framework (LSC4Rec) under a device-cloud collaboration setting. LSC4Rec aims to integrate the advantages of both LLMs and SRMs, as well as the benefits of cloud and edge computing, achieving a complementary synergy. We enhance the practicability of LSC4Rec by designing three strategies: collaborative training, collaborative inference, and intelligent request. During training, LLM generates candidate lists to enhance the ranking ability of SRM in collaborative scenarios and enables SRM to update adaptively to capture real-time user interests. During inference, LLM and SRM are deployed on the cloud and on the device, respectively. LLM generates candidate lists and initial ranking results based on user behavior, and SRM get reranking results based on the candidate list, with final results integrating both LLM's and SRM's scores. The device determines whether a new candidate list is needed by comparing the consistency of the LLM's and SRM's sorted lists. Our comprehensive and extensive experimental analysis validates the effectiveness of each strategy in LSC4Rec.