Question

Exercício4. Determine, por decomposição em fatores primos, o mmc de.
a) 18,27
c)18.30.48
b) 150,300​

Answer 1

$\Large\boxed{\begin{array}{l}\rm a)\\\begin{array}{c|c}\sf18,27&\sf2\\\sf9,27&\sf3\\\sf3,9&\sf3\\\sf1,3&\sf3\\\sf1,1\end{array}\\\sf mmc(18,27)=2\cdot3\cdot3\cdot3=54\\\rm b)\\\begin{array}{c|c}\sf18,30,48&\sf2\\\sf9,15,24&\sf2\\\sf9,15,12&\sf2\\\sf9,15,6&\sf2\\\sf9,15,3&\sf3\\\sf3,5,1&\sf3\\\sf1,5,1&\sf5\\\sf1,1,1\end{array}\\\sf mmc(18,30,48)=2^4\cdot3^2\cdot5\\\sf mmc(18,30,48)=16\cdot9\cdot5=720\end{array}}$

$\Large\boxed{\begin{array}{l}\rm c)\\\begin{array}{c|c}\sf150,300&\sf2\\\sf75,150&\sf2\\\sf75,75&\sf3\\\sf25,25&\sf5\\\sf5,5&\sf5\\\sf1,1\end{array}\\\sf mmc(150,300)=2^2\cdot3\cdot5^2\\\sf mmc(150,300)=4\cdot3\cdot25\\\sf mmc(150,300 )=300\end{array}}$