# They grew up so beautifully

**Number Theory**Level 4

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.