Three Toed Sloth

For some reason, whenever the Los Angeles Zoo has exhibited sloths in the past, it was always the two toed variety, never the three. Three toed sloths seem to have more standout facial markings.

in europe they are petty rare, i wonder why , i dont remember see much of the three ones in europe as well....

These are the only publicly displayed 3-toed in the US. In fact ISIS doesn't list any being held anywhere else. (Although ISIS doesn't list DWA as having them either.)

No Bradypus species is currently kept in any European zoo collection, as their husbandry is pretty problematic and finical, among others due to them being pretty picky folivores.
The last three-toed sloth in an European zoo so far was probably a confiscated male Pale-throated Sloth kept at Hannover Zoo in 1989.

Currently, most European zoos keep the much easier to feed & keep Linnaeus' two-toed sloth, and a few zoos also display Hoffmann's two-toed sloth.

On a side note: some pretty interesting yet also rather disgusting sloth behaviour. Be warned: after reading, you might look at those fuzzy "muppets" differently...
May two-toed sloths climb into your latrine and eat your faeces and urine, because that's the sort of thing they do : Tetrapod Zoology

I'm pretty sure there is one other facility in the US that has 3-toed.

It seems some years ago, that Chicago(Brookfield or Lincoln Park) kept and bred them quite successfully. I believe it was at the Brookfield Zoo, back in the 1970s.