Doti naturāli skaiţ̦i \(a, b, a^{\prime}, b^{\prime}\). Apzīmēsim \((a, b)\) ar \(d\) un \(a^{\prime}, b^{\prime}\) ar \(d^{\prime}\). Pierādīt, ka \(\left(a a^{\prime}, a b^{\prime}, b a^{\prime}, b b^{\prime}\right)=d d^{\prime}\).
Izmantojot LKD īpašības, iegūstam
\[\begin{aligned} & \left(a a^{\prime}, a b^{\prime}, b a^{\prime}, b b^{\prime}\right)=\left(\left(a a^{\prime}, a b^{\prime}\right),\left(b a^{\prime}, b b^{\prime}\right)\right)= \\ & \left(a\left(a^{\prime}, b^{\prime}\right), b\left(a^{\prime}, b^{\prime}\right)\right)=\left(a d^{\prime}, b d^{\prime}\right)=(a, b) d^{\prime}=d d^{\prime} \end{aligned}\]