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.

×

Problem Loading...

Note Loading...

Set Loading...