Can I put a Shimano SLX 12 gears cassette and SLX rear derailleur on road bike?
 

I am looking for the cheapest way of getting a 1x12 setup on a road bike. Will new 12 gear Shimano Slx work with shimano 105 shifters? By working I mean shifting all 12 gears.

Nope, the shifter only has 11 positions. Additionally, Shimano 10/11/12 speed mechanical MTB derailleurs are not compatible with road shifters.

12speed drivetrains are still new and as such, still pretty expensive. It is only recently that Shimano released a lower cost 12 speed MTB system and Sram has had their lower cost MTB systems in place for some time. At this point there is only Campagnolo and Sram that offers 12 speed drivetrains for drop bar bikes. Neither of which is considered cheap. There is a 13 speed set up but it's even more expensive.

The Sram Force/Red AXS controls with an Eagle AXS derailleur is really the only 1x12 system available.

If you wanted to save a few bucks and not replace your brake levers or calipers you could use the AXS Eagle derailleur with the blip box.

Sram Blip Box $385

Sram Etap remote blip switches Not necessary but would be nice, $110

Eagle XO1 AXS derailuer $700

Add on the chain and cassette of your choice and that would do it.

Just as an FYI:

Sram Force HRD AXS controls $495 each for front/rear

Since the question has been answered, the natural follow up is- why? Why 1x12?

Because it has more range than 1x11.

I can't answer for the OP, but I have been looking into it myself. The $2200+ price tag for a nice Force/XX1 set up is almost laughable. You can literally buy another bike for that much. I'm not interested until the price comes down.

I currently run a 1x Force set up with an E*13 9-46 MTB cassette. Big range cassettes come with big jumps in gearing. It would be nice to have a cassette with one more gear to ease the jumps a bit.

Yes- at that price, why 1x12. Lots of spending in this sport and hobby doesnt make sense, some of mine included.
So if this is just a time when someone wants something because they can, then cool.

But the price for what you get just isn't impressive. 2x gives you massive range and small jumps for 4x less cost.

Which is why the OP was seeing if it could be done a lot cheaper with SLX,

Yes you can.

https://www.gevenalle.com/product/hydraulic-1x12/

Interesting approach to install MTB derailleurs with drop bar controls. It looks like they just stuck an old indexed friction shifter to the front of a brake lever. Not a very elegant solution but it should work well enough. None of the options appear to be in stock at the moment though.

4x less cost? Only when comparing this AXS set up to a 105 or Rival system. Compare it to the new GRX Di2 or Ultegra Di2 and you'll notice the price difference isn't nearly as big.

The 1x vs. 2x debate will continue on but to me it all depends on how you ride your gravel bike. Since I ride mine more like an MTB the 1x set up lends itself pretty well to my riding style. The jumps in gearing aren't a deal breaker by any means. And shifting a front derailleur under load on a regular basis is a recipe for disaster.

The only reason for me to upgrade at this point is I want to try electronic shifting. Maybe AXS, maybe GRX. Maybe even a 2x. But for now I'll stick with what I got.

Exactly. If 11 is enough for Nigel Tufnel, it’s enough for me.

https://www.archercomponents.com/
That would also work