I want to know the extent of his use of the drum machines (mostly which most recent songs use them). I know all of the 1999 album but when did he last use the LM 1?

Also, where can I buy an LM1?

I'll take the high road on this one....
IIRC Clouds & Gold Standard from AOA are the last songs with linn drum.
20ten & MPLsound (2009) are all linn based songs.
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As for where to buy one, there are a couple on Reverb at the moment, probably around 30k usd. Kinda pricy! Easier to get a hold of an LM-2. Alternatively, there are modern replicas available like the Luma1 from around 5k usd.

Most of us make do with samples from the LM-1 and Linndrum, or use some of the many VSTs which attempt to emulate them in software. AJ Lab for example.

I would recommend the LM-1 Samples From Mars pack, they sourced sounds from two LM-1's - processed and raw sounds, different tunings, filters and all. Even includes a rare crash sound Quincy Jones supposedly installed on one of the LM-1's!

Comes with individual folders for different DAWs & samplers, including for Ableton, FL Studio, Akai MPC and all... Worth a shot!

There is also a Luma-1 clone of the Linn LM-1 being developed, of which only 100 were made so far. It's a slightly more advanced version with tuning & pan knobs on the front panel (Prince would have certainly loved that), ability to load alternate sounds from files etc. But it's slightly less expensive than the real Linn, about 5k or so.