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Question-30646

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Question Number 30646 by mondodotto@gmail.com last updated on 23/Feb/18
Commented by Rasheed.Sindhi last updated on 23/Feb/18
The third number is 108
$$\mathrm{The}\:\mathrm{third}\:\mathrm{number}\:\mathrm{is}\:\mathrm{108} \\ $$
Commented by mondodotto@gmail.com last updated on 23/Feb/18
please share your solution
$$\mathrm{please}\:\mathrm{share}\:\mathrm{your}\:\mathrm{solution} \\ $$
Answered by Rasheed.Sindhi last updated on 24/Feb/18
LCM:432=2^4 ×3^3 GCF:12=2^2 ×3 36=2^2 ×3^2 48=2^4 ×3 X=2^m ×3^n : 2≤m≤4 , 1≤n≤3 LCM(2^2 ×3^2 , 2^4 ×3 , 2^m ×3^n )=2^4 ×3^3 max(2,4,m)=4⇒m=1,2,3,4 −−A max(2,1,n)=3⇒n=3 GCF(2^2 ×3^2 , 2^4 ×3 , 2^m ×3^n )=2^2 ×3 min(2,4,m)=2⇒m=2,3,... −−B From A & B : m=2,3,4 X=2^(2,3,4) ×3^3 X=2^2 ×3^3 =108 or X=2^3 ×3^3 =216 or X=2^4 ×3^3 =432
$$\mathrm{LCM}:\mathrm{432}=\mathrm{2}^{\mathrm{4}} ×\mathrm{3}^{\mathrm{3}} \\ $$$$\mathrm{GCF}:\mathrm{12}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3} \\ $$$$\mathrm{36}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3}^{\mathrm{2}} \\ $$$$\mathrm{48}=\mathrm{2}^{\mathrm{4}} ×\mathrm{3} \\ $$$$\mathrm{X}=\mathrm{2}^{\mathrm{m}} ×\mathrm{3}^{\mathrm{n}} \::\:\mathrm{2}\leqslant\mathrm{m}\leqslant\mathrm{4}\:,\:\mathrm{1}\leqslant\mathrm{n}\leqslant\mathrm{3} \\ $$$$\mathrm{LCM}\left(\mathrm{2}^{\mathrm{2}} ×\mathrm{3}^{\mathrm{2}} ,\:\mathrm{2}^{\mathrm{4}} ×\mathrm{3}\:,\:\mathrm{2}^{\mathrm{m}} ×\mathrm{3}^{\mathrm{n}} \right)=\mathrm{2}^{\mathrm{4}} ×\mathrm{3}^{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{max}\left(\mathrm{2},\mathrm{4},\mathrm{m}\right)=\mathrm{4}\Rightarrow\mathrm{m}=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\:−−\mathrm{A} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{max}\left(\mathrm{2},\mathrm{1},\mathrm{n}\right)=\mathrm{3}\Rightarrow\mathrm{n}=\mathrm{3} \\ $$$$\mathrm{GCF}\left(\mathrm{2}^{\mathrm{2}} ×\mathrm{3}^{\mathrm{2}} ,\:\mathrm{2}^{\mathrm{4}} ×\mathrm{3}\:,\:\mathrm{2}^{\mathrm{m}} ×\mathrm{3}^{\mathrm{n}} \right)=\mathrm{2}^{\mathrm{2}} ×\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{min}\left(\mathrm{2},\mathrm{4},\mathrm{m}\right)=\mathrm{2}\Rightarrow\mathrm{m}=\mathrm{2},\mathrm{3},…\:\:−−\mathrm{B} \\ $$$$\mathrm{From}\:\mathrm{A}\:\&\:\mathrm{B}\::\:\mathrm{m}=\mathrm{2},\mathrm{3},\mathrm{4} \\ $$$$\mathrm{X}=\mathrm{2}^{\mathrm{2},\mathrm{3},\mathrm{4}} ×\mathrm{3}^{\mathrm{3}} \\ $$$$\mathrm{X}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3}^{\mathrm{3}} =\mathrm{108} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{or} \\ $$$$\mathrm{X}=\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{3}} =\mathrm{216} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{or} \\ $$$$\mathrm{X}=\mathrm{2}^{\mathrm{4}} ×\mathrm{3}^{\mathrm{3}} =\mathrm{432} \\ $$
Commented by mondodotto@gmail.com last updated on 24/Feb/18
thank you sir i appriciate this
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}\:\mathrm{i}\:\mathrm{appriciate}\:\mathrm{this} \\ $$
Commented by rahul 19 last updated on 24/Feb/18
appreciate^∗
$$\mathrm{appreciate}\:^{\ast} \\ $$
Commented by Rasheed.Sindhi last updated on 24/Feb/18
tђคภк א๏ย ๒๏tђ!

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