It is wrong, the “smallest number that divides” any number is always just 1. I had LCDS (lowest common denominators?) and it took me a while to see my mistake, DR. BLACKWELL seemed plausible.
Looks like I'm the one who 'divide' has tripped up! Apologies guys - I've updated the clue with something that hopefully works okay. (@SM I think 0.5 divides all integers, for that matter )