Răspuns:
257
Explicație pas cu pas:
[tex]D:24 = C_1\text{ rest }17\\ D:48 = C_2\text{ rest }17\\D:40 = C_3\text{ rest }17\\ \\ D = 24\cdot C_1+17 \\ D = 48\cdot C_2+17 \\ D = 40\cdot C_3+17\\ \\ 24\cdot C_1 = 48\cdot C_2 = 40\cdot C_3 \\ \\ \mathrm{cmmmc}(24,\,48,\,40) = \mathrm{cmmmc}(2^3\cdot 3,\,2^4\cdot 3,\,2^3\cdot 5)=\\ \\ =2^4\cdot 3\cdot 5 = 240 \\ \\ \dfrac{240}{48} = 5,\quad \dfrac{240}{40} = 6,\quad \dfrac{240}{24} = 10\\ \\ \Rightarrow C_1 = 10,\quad C_2 = 5,\quad C_3 = 6 \\ \\ \Rightarrow D = 24\cdot 10+17 = 257[/tex]
