I'm too lazy to work it out, thanks haha

I think it depends on what stats you started with (unless it was the same for all, I never noticed). I would imagine most or all the skills at 100 since 81 is a pretty high level.

Is this a trick question? All of them. All 18 of you skills need to be at 100 for you to be at max level 81.

Well, all level 81's I've made, have 80 skill points to distribute. All of them, had to max all their skills to 100.

The Skill I found the hardest to levelup, was speech -at first. Things changed when I realized that you gain experience, not only by selling, but also buying expensive items.
Arcadia would've lots of stories to tell about the Dragonborn, buying all her ingredients, crafting potions, selling them to her, only to buy them back and sell them again, etc.

That's not how it works.

Your level will be 81 when all skills are at 100. 81 isn't a set cap; 81 is the result of all skills at 100.

You get to Level 81 somewhat before you level everything to 100.

You need 89000 XP points to get to level 81.
If you level one tree to 100, you get 5049 XP points
If you level all 18 trees to 1000, you get 90882 XP points.

So, if you have 17 skills at level 99 and one skill at 100, you just barely make it to level 81.
Or, if you have 17 skills at level 100, you can have the last skill at level 80 and make to level 81.