Question Number 33090 by jasno91 last updated on 10/Apr/18
Answered by MJS last updated on 10/Apr/18
$${gcd}\left(\mathrm{663};\mathrm{975}\right)= \\ $$$$={gcd}\left(\mathrm{3}×\mathrm{13}×\mathrm{17};\mathrm{3}×\mathrm{5}^{\mathrm{2}} ×\mathrm{13}\right)= \\ $$$$=\mathrm{39} \\ $$$$ \\ $$$${lcm}\left(\mathrm{9};\mathrm{21}\right)={lcm}\left(\mathrm{3}^{\mathrm{2}} ;\mathrm{3}×\mathrm{7}\right)=\mathrm{63} \\ $$$$\mathrm{63}{n}<\mathrm{1000}\:\Rightarrow\:{n}=\mathrm{15} \\ $$$$\mathrm{63}×\mathrm{15}=\mathrm{945} \\ $$$$ \\ $$$${lcm}\left(\mathrm{12};\mathrm{32};\mathrm{48}\right)= \\ $$$$={lcm}\left(\mathrm{2}^{\mathrm{2}} ×\mathrm{3};\mathrm{2}^{\mathrm{5}} ;\mathrm{2}^{\mathrm{4}} ×\mathrm{3}\right)=\mathrm{96} \\ $$$$\mathrm{96}{n}<\mathrm{10000}\:\Rightarrow\:{n}=\mathrm{104} \\ $$$$\mathrm{96}×\mathrm{104}=\mathrm{9984} \\ $$$$ \\ $$$${lcm}\left(\mathrm{12};\mathrm{16};\mathrm{20}\right)= \\ $$$$={lcm}\left(\mathrm{2}^{\mathrm{2}} ×\mathrm{3};\mathrm{2}^{\mathrm{4}} ;\mathrm{2}^{\mathrm{2}} ×\mathrm{5}\right)=\mathrm{240} \\ $$