Question

Calculați c.m.m.d.c. şi c.m.m.m.c. pentru numerele 180 și 450.Va rogg!!

Answer 1

$180 = 2\times 90 = 2\times 3\times 30 = 2\times 3\times 3\times 10 = 2\times 3^2\times 2\times 5 = \\ \\ = 2^2\times 3^2\times 5 \\ \\ 450 = 5\times 90 = 5\times 9\times 10 = 5\times 3^2\times 2\times 5 = 2\times 3^2\times 5^2$

$\Rightarrow \left\| \begin{array}{c}190 = 2^2\times 3^2\times 5 \\ 450 = 2\times 3^2\times 5^2 \end{array} \right| \Rightarrow \left\| \begin{array}{c}\text{c.m.m.d.c.(180, 450)}=2 \quad \quad \quad \quad \\ \text{c.m.m.m.c.(180, 450)}= 2^2\times 3^2\times 5^2\end{array} \right|\Rightarrow$

$\Rightarrow \left\| \begin{array}{c}\text{c.m.m.d.c.(180, 450)}=2 \quad \quad \quad \quad \\ \text{c.m.m.m.c.(180, 450)}= 900\quad \quad\quad\quad\end{array} \right|$