GCD{$\ \cdot\ $}LCM = PROD:For {$T\in\mathcal{B}^+$}, {$$\text{GCD}_{_T}\cdot\text{LCM}_{_T}=\text{PROD}_{_T}.$$} Proof: The Theorem for Axles: If {$T\in\mathcal {B}^+$} is an axle, then {$$\text{GCD}_{_T}\cdot\text{LCM}_{_T}=\text{PROD}_{_T}.$$} The Theorem for Rims: If {$T\in\mathcal {B}^+$} is a rim, then {$$\text{GCD}_{_T}\cdot\text{LCM}_{_T}=\text{PROD}_{_T}.$$} The Theorem for Spokes: If {$T\in\mathcal {B}^+$} is a spoke, then {$$\text{GCD}_{_T}\cdot\text{LCM}_{_T}=\text{PROD}_{_T}.$$} The Theorem for Generic Boxes: If {$T\in\mathcal {B}^+$} is generic, then {$$\text{GCD}_{_T}\cdot\text{LCM}_{_T}=\text{PROD}_{_T}.$$} |