VLookup Across Multiple Sheets - How do you return a Minimum Value or Sheet Name?

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Unless each worksheet contains the name of the vendor somewhere on it, then this formula is going to get much much uglier.
I'm not sure there's a formulaic way to reference the tab name outside of cell("filename"), and stripping the filename down to single tab is rough.

I'd recommend opting for a VBA approach, which would have the added benefit of also eliminating the volatility of using a number of INDIRECT functions.

Here's the brief code I used, and a sample workbook I put together.

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If your data is sensitive in nature, I'd highly recommend creating an example from scratch that would apply to your solution for others to use.
Column Headers, fantasy tab names, and pretend values on the columns required is all that's needed.