Can I run SmolLM3-3B on an RTX 5060?

Yes, just

Its published weights (6.15 GB) fit in the 7.20 GB an RTX 5060 can use, with room for ≈ 14K tokens of context.

hf download HuggingFaceTB/SmolLM3-3B

Files and context on RTX 5060

Each file of SmolLM3-3B (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.

SmolLM3-3B on other hardware

Popular models that run on RTX 5060

Assumes 90% of the card's memory is usable and at least 4K tokens of context for one conversation, with the context cache in 16-bit unless noted. Fits leaves at least 20% of that memory for context; Tight leaves less.