Question

знайти НСК 144і420, НСД 15999і1600

Answer 1

${\begin{array}{l}{\begin{array}{r|r}144&2 \\ 72&2 \\ 36&2 \\ 18&2 \\ 9&3 \\ 3&3 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}&&{\begin{array}{l}{\begin{array}{r|l}420&2 \\ 210&2 \\ 105&3 \\ 35&5 \\ 7&7 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \phantom{8} \\ \end{array}} \\ \end{array}}$

$144=2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3=2^{4}\cdot3^{2}\\420=2\cdot 2\cdot 3\cdot 5\cdot 7=2^{2}\cdot 3\cdot 5\cdot7$

НСК(144,420)=2⁴⋅3²⋅5⋅7=5040

${\begin{array}{l}{\begin{array}{r|r}15999&3 \\ 5333&5333 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \phantom{8} \\ \phantom{8} \\ \phantom{8} \\ \phantom{8} \\ \phantom{8} \\ \phantom{8} \\ \end{array}} \\ \end{array}}&{\begin{array}{l}{\begin{array}{r|l}1600&2 \\ 800&2 \\ 400&2 \\ 200&2 \\ 100&2 \\ 50&2 \\ 25&5 \\ 5&5 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}$

$15999=3\cdot 5333\\1600=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 5\cdot 5=2^{6}\cdot 5^{2}$

НCД(15999,1600)=1