Least Common Multiple - LCM: Very Difficult Problems with Solutions

Solution:
[tex]LCM(360;18;245)=LCM(LCM(360;18);245)=LCM(360;245)[/tex]. We have:
[tex]360=2^3 \cdot 3^2 \cdot 5^1[/tex]
[tex]245=2^0 \cdot 3^0 \cdot 5^1 \cdot 7^2[/tex] We take the highest exponent for each base and the result is [tex]LCM(360;245;18)=2^3 \cdot 3^2 \cdot 5^1 \times 7^2=360 \cdot 49=17640[/tex]

Solution:
[tex]L=LCM(2;3;4;5;6;7;8)=LCM(2;4;8;3;6;5;7)[/tex]. Since 5 and 7 are coprime with all other numbers, we can pull them out before the LCM function: [tex]L=5 \times 7 \times LCM(2;4;8;3;6)=35 \times LCM(LCM(2;4;8);LCM(3;6))=35 \cdot LCM(8;6)=35 \cdot 24=840[/tex]