Question

нск і нсд (72,96,120)​

Answer 1

Ответ:

НСК(72,96,120)=1440

НCД(72,96,120)=24

Пошаговое объяснение:

${\begin{array}{l}{\begin{array}{r|r}72&2 \\ 36&2 \\ 18&2 \\ 9&3 \\ 3&3 \\ 1&\;\end{array}} \\ {\begin{array}{l}\phantom{8} \\ \phantom{8}\end{array}} \end{array}}&{\begin{array}{l}{\begin{array}{r|l}96&2 \\ 48&2 \\ 24&2 \\ 12&2 \\ 6&2 \\ 3&3 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}&{\begin{array}{l}{\begin{array}{r|l}120&2 \\ 60&2 \\ 30&2 \\ 15&3 \\ 5&5 \\ 1&\; \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \phantom{8}\end{array}}\end{array}}$

$72=2^{3}\cdot3^{2}\\96=2^{5}\cdot3\\120=2^{3}\cdot 3\cdot5$

НСК(72,96,120)=2⁵⋅3²⋅5=1440

НCД(72,96,120)=2³·3=24