# Hardest Multiple Ever!

$\dfrac{abc}{a-\dfrac{1}{b-\dfrac{1}{c}}} = 15,\qquad \dfrac{abc}{c-\dfrac{1}{a-\dfrac{1}{b}}} = 6, \qquad \dfrac{abc}{b-\dfrac{1}{c-\dfrac{1}{a}}} = 4$

Given that $$a, b$$ and $$c$$ are integers satisfying the system of equations above, what is the value of $$\text{lcm}(a, b, c)$$?

Notation: $$\text{lcm}$$ stands for Lowest Common Multiple.

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