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.

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