Question

aflati nr natural xy, x diferit 0, stiind ca (xy,96)=12 si (xy,70)=14

Answer 1

Explicație pas cu pas:

96 = 12×8

$\overline {xy} = 12 \cdot m \ , \ (m,8) = 1$

$10 \leqslant \overline {xy} \leqslant 99 \implies m \in \Big\{ 3; 5; 7 \Big\}$

$\implies \overline {xy} \in \Big\{ 36; 60; 84 \Big\}$

70 = 14×5

$\overline {xy} = 14 \cdot n \ , \ (n,5) = 1$

$10 \leqslant \overline {xy} \leqslant 99 \implies n \in \Big\{ 1; 2; 3; 4; 6; 7 \Big\}$

$\implies \overline {xy} \in \Big\{ 14; 28; 42; 56; 84; 98 \Big\}$

unica soluție este:

$\overline {xy} = 84$