Question

Alguém pode me dizer a diferença entra mmc e fatoração de números inteiros por favor.

Answer 1

$\large\boxed{\begin{array}{l}\rm A\,fatorac_{\!\!,}\tilde ao\,de\,um\,n\acute umero~pode\,ocorrer\\\rm de\,v\acute arias\,maneiras. No\,entanto,a\,mais\,utilizada\\\rm \acute e\,a\,decomposic_{\!\!,}\tilde ao\,em\,fatores\,primos\\\rm que\,conforme\,o\,nome\,diz,representa\\\rm um\,determinado\,n\acute umero\\\rm escrito\,como\,multiplicac_{\!\!,}\tilde ao\,de\,n\acute umeros\,primos.\end{array}}$

$\large\boxed{\begin{array}{l}\rm Por\,exemplo~podemos\,dizer\,que\,48=8\cdot 6\\\rm mas\,este\,n\acute umero\,n\tilde ao\,est\acute a\,escrito\,como\\\rm multiplicac_{\!\!,}\tilde ao\,de\,fatores\,primos\\\rm pois\,6\,e\,8\,n\tilde ao\,s\tilde ao\,primos.\\\rm No\,entanto\,quando\,afirmamos\,que\\\rm 48=2^4\cdot3\\\rm estamos\,escrevendo\,o\,48\\\rm como\,multiplicac_{\!\!,}\tilde ao\,de\,n\acute umeros\,primos.\\\rm isto\,\acute e\\\rm 48\,foi\,decomposto\,em\,fatores\,primos.\end{array}}$

$\large\boxed{\begin{array}{l}\rm O\,m\cdot m\cdot c~representa\,o\,menor\,m\acute ultiplo\\\rm comum\,entre\,dois\,ou\,mais\,n\acute umeros.\\\rm Para\,determinar\,o\,m\cdot m\cdot c\\\rm de\,dois\,ou\,mais\,n\acute umeros\\\rm usamos\,a\,decomposic_{\!\!,}\tilde ao\,em\,fatores\,primos\\\rm que\,pode\,ser\,simult\hat anea\,ou\,n\tilde ao.\end{array}}$

$\large\boxed{\begin{array}{l}\rm Exemplo: Utilize\,a\,decomposic_{\!\!,}\tilde ao\,simult\hat anea\\\rm em\,fatores\,primos\,e\,calcule~m\cdot m\cdot c(4,8,12).\\\underline{\sf soluc_{\!\!,}\tilde ao}\\\rm\\\begin{array}{c|c}\rm4,8,12&\rm2\\\rm2,4,6&\rm2\\\rm1,2,3&\rm2\\\rm1,1,3&\rm3\\\rm1,1,1\end{array}\\\rm m\cdot m\cdot c(4,8,12)=2^3\cdot3=8\cdot3=24\end{array}}$

$\large\boxed{\begin{array}{l}\rm Calcule\,o\,m\cdot m\cdot c\,do\,exemplo\,anterior\\\rm sem\,usar\,decomposic_{\!\!,}\tilde ao\,simult\hat anea.\\\underline{\sf soluc_{\!\!,}\tilde ao}\\\begin{array}{c|c}\rm4&\rm2\\\rm2&\rm2\\\rm1\end{array}\\\rm 4=2^2\\\begin{array}{c|c}\rm8&\rm2\\\rm4&\rm2\\\rm2&\rm2\\\rm1\end{array}\\\rm 8=2^3\\\begin{array}{c|c}\rm12&\rm2\\\rm6&\rm2\\\rm3&\rm3\\\rm1\end{array}\\\rm 12=2^2\cdot3\end{array}}$

$\large\boxed{\begin{array}{l}\rm O\,m\cdot m\cdot c\,\acute e\,o\,produto\,dos\,fatores\\\rm comuns\,tomados\,ao\,maior\,expoente\\\rm pelos\,fatores\,n\tilde ao-comuns.\\\rm ou \,seja\\\rm m\cdot m\cdot c(4,8,12)=2^3\cdot3=24\end{array}}$

$\large\boxed{\begin{array}{l}\rm resumindo:\\\bf{fatorac_{\!\!,}}\tilde ao: \rm consiste\,em\,escrever\\\rm um\,n\acute umero\,como\,produto\,de\,n\acute umeros\,primos.\\\\\bf{ m\cdot m\cdot c}:\rm \acute E\,necess\acute ario\,ao\,ao\,menos\,dois\,n\acute umeros\\\rm para\,calcular\\\rm consiste\,em\,exibir\,o\,menor\,m\acute ultiplo\,comum\\\rm entre\,dois\,ou\,mais\,n\acute umeros.\end{array}}$