# They grew up so beautifully

Find the number of solutions to $$[a,b,c](a,b,c) = \sqrt{abc}$$ where $$a\geq b \geq c$$ are integers ranging from $$1$$ to $$30$$.

Here $$[a,b,c]$$ and $$(a,b,c)$$ are the least common multiple (LCM) and the greatest common divisor (GCD) of $$a,b,c$$ respectively.

×