Question

Hallar el minimo común múltiplo mcm (24, 54, 60) mcm (120, 80, 60) mcm (20, 15, 8) mcm (24, 36, 48) paso a paso gracias ​

Answer 1

Determinaremos el mínimo común múltiplo(m.c.m.) por descomposición simultánea.

✎ mcm(24, 54, 60)

                                             $\begin{array}{ccccc|c}\blue{\boldsymbol{\sf{24}}}&&\blue{\boldsymbol{\sf{54}}}&&\blue{\boldsymbol{\sf{60}}}&\sf{2}\\\sf{12}&&\sf{27}&&\sf{30}&\sf{2}\\\sf{6}&&\sf{27}&&\sf{15}&\sf{2}\\\sf{3}&&\sf{27}&&\sf{15}&\sf{3}\\\sf{1}&&\sf{9}&&\sf{5}&\sf{3}\\\sf{1}&&\sf{3}&&\sf{5}&\sf{3}\\\sf{1}&&\sf{1}&&\sf{5}&\sf{5}\\\sf{1}&&\sf{1}&&\sf{1}&\end{array}$

                           $\begin{array}{c}\sf{m.c.m.(24, 54, 60)=2\times2\times2\times3\times3\times3\times5}\\\\\mathsf{m.c.m.(24, 54, 60)=2^{3}\times3^{3}\times5^{}}\\\\\boxed{\boxed{\boldsymbol{\mathsf{m.c.m.(24, 54, 60)=1080}}}}\end{array}$

Rpta. El mínimo común múltiplo de 24, 54 y 60 es 1080

✎ mcm(120, 80, 60)

                                              $\begin{array}{ccccc|c}\blue{\boldsymbol{\sf{120}}}&&\blue{\boldsymbol{\sf{80}}}&&\blue{\boldsymbol{\sf{60}}}&\sf{2}\\\sf{60}&&\sf{40}&&\sf{30}&\sf{2}\\\sf{30}&&\sf{20}&&\sf{15}&\sf{2}\\\sf{15}&&\sf{10}&&\sf{15}&\sf{2}\\\sf{15}&&\sf{5}&&\sf{15}&\sf{3}\\\sf{5}&&\sf{5}&&\sf{5}&\sf{5}\\\sf{1}&&\sf{1}&&\sf{1}&\end{array}$

                              $\begin{array}{c}\sf{m.c.m.(120, 80, 60)=2\times2\times2\times2\times3\times5}\\\\\mathsf{m.c.m.(120, 80, 60)=2^{4}\times3^{}\times5^{}}\\\\\boxed{\boxed{\boldsymbol{\mathsf{m.c.m.(120, 80, 60)=240}}}}\end{array}$

Rpta. El mínimo común múltiplo de 120, 80 y 60 es 240

✎ mcm (20, 15, 8)

                                               $\begin{array}{ccccc|c}\blue{\boldsymbol{\sf{20}}}&&\blue{\boldsymbol{\sf{15}}}&&\blue{\boldsymbol{\sf{8}}}&\sf{2}\\\sf{10}&&\sf{15}&&\sf{4}&\sf{2}\\\sf{5}&&\sf{15}&&\sf{2}&\sf{2}\\\sf{5}&&\sf{15}&&\sf{1}&\sf{3}\\\sf{5}&&\sf{5}&&\sf{1}&\sf{5}\\\sf{1}&&\sf{1}&&\sf{1}&\end{array}$

                                  $\begin{array}{c}\sf{m.c.m.(20, 15, 8)=2\times2\times2\times3\times5}\\\\\mathsf{m.c.m.(20, 15, 8)=2^{3}\times3^{}\times5^{}}\\\\\boxed{\boxed{\boldsymbol{\mathsf{m.c.m.(20, 15, 8)=120}}}}\end{array}$

Rpta. El mínimo común múltiplo de 20, 15 y 8 es 120

✎ mcm (24, 36, 48)          

                                           $\begin{array}{ccccc|c}\blue{\boldsymbol{\sf{24}}}&&\blue{\boldsymbol{\sf{36}}}&&\blue{\boldsymbol{\sf{48}}}&\sf{2}\\\sf{12}&&\sf{18}&&\sf{24}&\sf{2}\\\sf{6}&&\sf{9}&&\sf{12}&\sf{2}\\\sf{3}&&\sf{9}&&\sf{6}&\sf{2}\\\sf{3}&&\sf{9}&&\sf{3}&\sf{3}\\\sf{1}&&\sf{3}&&\sf{1}&\sf{3}\\\sf{1}&&\sf{1}&&\sf{1}&\end{array}$

                            $\begin{array}{c}\sf{m.c.m.(24, 36, 48)=2\times2\times2\times2\times3\times3}\\\\\mathsf{m.c.m.(24, 36, 48)=2^{4}\times3^{2}}\\\\\boxed{\boxed{\boldsymbol{\mathsf{m.c.m.(24, 36, 48)=144}}}}\end{array}$

Rpta.  El mínimo común múltiplo de 24, 36 y 48 es 144

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