Question

Halla el M.C.M y el M.C.D de: a)48 24/2 b)240 1600/2 c)1300 156/2​

Answer 1

En orden alfabetico:

A)

MCM de 48 24

$\large\displaystyle\begin{gathered}\sf \left.\begin{matrix} \blue{48 \ \ \ 24}\\ 24 \ \ \ 12\\ 12 \ \ \ \ 6\\ \ 6 \ \ \ \ 3\\ \ 3 \ \ \ \ 3\\ \ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 2\\ 3\\ \: \end{matrix} \end{gathered}$

$\sf{m.c.m.(24,48)=2\times2\times2\times2\times3}$

$\sf{m.c.m.(24,48)=2^{4} \times3}$

$\boxed{\boxed{\sf{m.c.m.(48,24)=48}}}$

↓

MCD de 48 24

$\large\displaystyle\begin{gathered}\sf \left.\begin{matrix} \blue{48 \ \ \ 24}\\ 24 \ \ \ 12\\ 12 \ \ \ \ 6\\ \ 6 \ \ \ \ 3\\ \ 2 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 3\\ \: \end{matrix} \end{gathered}$

$\sf{m.c.d.(24,48)=2\times2\times2\times3}$

$\sf{m.c.m.(24,48)=2^{3} \times3}$

$\boxed{\boxed{\sf{m.c.d.(48,24)=24}}}$

================================================================

B)

MCM de 240 y 1600

$\large\displaystyle\begin{gathered}\sf \left.\begin{matrix} \blue{240\ \ \ 1600}\\ 120 \ \ \ \ 800\\ \ 60 \ \ \ \ 400\\ \ 30 \ \ \ \ 200\\ \ 15 \ \ \ \ 100\\ \ 15 \ \ \ \ \ 50\\ \ 15 \ \ \ \ \ 25\\ \ \ 5 \ \ \ \ \ 25\\ \ \ 1 \ \ \ \ \ \ 5\\ \ \ 1 \ \ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 2\\ 2\\ 2\\ 3\\ 5\\ 5\\ \: \end{matrix} \end{gathered}$

$\sf{m.c.m.(240,1600)=2^{6}\times3\times5^{2} }$

$\boxed{\boxed{\sf{m.c.m.(240,1600)=4800}}}$

↓

MCD de 240 y 1600

$\large\displaystyle\begin{gathered}\sf \left.\begin{matrix} \blue{240 \ \ \ 1600}\\ 120 \ \ \ \ 800\\ \ 60 \ \ \ \ 400\\ \ 30 \ \ \ \ 200\\ \ 15 \ \ \ \ 100\\ \ 3 \ \ \ \ \ \ 20 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 2\\ 5\\ \: \end{matrix} \end{gathered}$

$\sf{m.c.d.(240,1600)=2\times2\times2\times2\times5}$

$\sf{m.c.d.(240,1600)=2^{3} \times5}$

$\boxed{\boxed{\sf{m.c.d.(240,1600)=80}}}$

================================================================

C)

MCM de 1300 y 156

$\large\displaystyle\begin{gathered}\sf \left.\begin{matrix} \blue{1300 \ \ 156}\\ \ 650 \ \ \ \ 78\\ \ 325 \ \ \ \ 39\\ \ 325 \ \ \ \ 13\\ \ \ 65 \ \ \ \ 13\\ \ \ 13 \ \ \ \ 13\\ \ \ \ 1 \ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 3\\ 5\\ 5\\ 13\\ \: \end{matrix} \end{gathered}$

$\sf{m.c.m.(1300,156)=2\times2\times3\times5\times5\times13}$

$\sf{m.c.m.(1600,156)=2^{2}\times3\times5^{2}\times13 }$

$\boxed{\boxed{\sf{m.c.m.(1300,56)=3900}}}$

↓

MCD de 1300 y 156

$\large\displaystyle\begin{gathered}\sf \left.\begin{matrix} \blue{1300 \ \ \ 156}\\ \ 650 \ \ \ \ 78\\ \ 325 \ \ \ \ 39\\ \ \ 25 \ \ \ \ \ 3 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 13\\ \: \end{matrix} \end{gathered}$

$\sf{m.c.d.(1300,156)=2\times2\times13}$

$\sf{m.c.d.(1300,156)=2^{2} \times13}$

$\boxed{\boxed{\sf{m.c.d.(1300,56)=52}}}$

Espero te sirva, Salu2!!!!!