En primer lugar, factorizamos los números
 
$120 = 2^{3}\cdot3\cdot5$
$330 = 2\cdot3\cdot5\cdot11$
$450 = 2\cdot3^{2}\cdot5^{2}$
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Buscamos los factores comunes a todos los números: 2 , 3 , 5 ,
y los elevamos a los menores exponentes
$M.C.D. ( 120 , 330 , 450 ) = 2\cdot3\cdot5 = 30$

$\left. \begin{array}{c|c}120 & 2\cr60 & 2 \cr30 & 2 \cr15 & 3 \cr5 & 5 \cr1\end{array} \right. \quad$$\left. \begin{array}{c|c}330 & 2\cr165 & 3 \cr55 & 5 \cr11 & 11 \cr1\end{array} \right. \quad$$\left. \begin{array}{c|c}450 & 2\cr225 & 3 \cr75 & 3 \cr25 & 5 \cr5 & 5 \cr1\end{array} \right. \quad$