Question

Calcule o m.m.c. fazendo a decomposição simultânea em fatores primos:

a) m.m.c. (10,12,15)
b) m.m.c. (25,30,40)
c) m.m.c. (64,128)
d) m.m.c. (88,100)​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\mathsf{ a)\ m\cdot m\cdot c\,(10,12,15)=60}$

$\mathsf{\begin{array}{r|l}\sf10,12,15&\sf2\\\sf5,6,15&\sf2\\\sf5,3,15&\sf3\\\sf5,1,5&\sf5\\\sf1,1,1&\overline{\sf2^2\cdot3\cdot5=60}\end{array}}$

$\mathsf{ b)\ m\cdot m\cdot c\,(25,30,40)=600}$

$\mathsf{\begin{array}{r|l}\sf25,30,40&\sf2\\\sf25,15,20&\sf2\\\sf25,15,10&\sf2\\\sf25,15,5&\sf3\\\sf25,5,5&\sf5\\\sf5,1,1&\sf5\\\sf1,1,1&\overline{\sf2^3\cdot3\cdot5^2=600}\end{array}}$

$\mathsf{ c)\ m\cdot m\cdot c\,(64,128)=128}$

$\mathsf{\begin{array}{r|l}\sf64,128&\sf2\\\sf32,64&\sf2\\\sf16,32&\sf2\\\sf8,16&\sf2\\\sf4,8&\sf2\\\sf2,4&\sf2\\\sf1,2&\sf2\\\sf1,1&\overline{\sf2^7=128}\end{array}}$

$\mathsf{ d)\ m\cdot m\cdot c\,(88,100)=2200}$

$\mathsf{\begin{array}{r|l}\sf88,100&\sf2\\\sf44,50&\sf2\\\sf22,25&\sf2\\\sf11,25&\sf5\\\sf11,5&\sf5\\\sf11,1&\sf11\\\sf1,1&\overline{\sf2^3\cdot5^2\cdot11=2200}\end{array}}$