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Question Number 74456 by liki last updated on 24/Nov/19

Commented by liki last updated on 24/Nov/19

...plz anyone knowing simple logic of  find the possible number,because    this always i did not understand so pl    i need simple way of find the others no.

$$...{plz}\:{anyone}\:{knowing}\:{simple}\:{logic}\:{of} \\ $$$${find}\:{the}\:{possible}\:{number},{because}\: \\ $$$$\:{this}\:{always}\:{i}\:{did}\:{not}\:{understand}\:{so}\:{pl}\: \\ $$$$\:{i}\:{need}\:{simple}\:{way}\:{of}\:{find}\:{the}\:{others}\:{no}. \\ $$

Commented by $@ty@m123 last updated on 24/Nov/19

there is no hard and fast rule.  Logic & method of solving problem  may vary from question to question.  You can learn this only   through practice.

$${there}\:{is}\:{no}\:{hard}\:{and}\:{fast}\:{rule}. \\ $$$${Logic}\:\&\:{method}\:{of}\:{solving}\:{problem} \\ $$$${may}\:{vary}\:{from}\:{question}\:{to}\:{question}. \\ $$$${You}\:{can}\:{learn}\:{this}\:{only}\: \\ $$$${through}\:{practice}. \\ $$

Answered by mr W last updated on 24/Nov/19

6=2^1 ×3^1   360=2^3 ×3^2 ×5^1     18=2^1 ×3^2   60=2^2 ×3^1 ×5^1   y=2^3 ×3^(1..2) ×5^(0..1) =24,72,120,360

$$\mathrm{6}=\mathrm{2}^{\mathrm{1}} ×\mathrm{3}^{\mathrm{1}} \\ $$$$\mathrm{360}=\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{2}} ×\mathrm{5}^{\mathrm{1}} \\ $$$$ \\ $$$$\mathrm{18}=\mathrm{2}^{\mathrm{1}} ×\mathrm{3}^{\mathrm{2}} \\ $$$$\mathrm{60}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3}^{\mathrm{1}} ×\mathrm{5}^{\mathrm{1}} \\ $$$${y}=\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{1}..\mathrm{2}} ×\mathrm{5}^{\mathrm{0}..\mathrm{1}} =\mathrm{24},\mathrm{72},\mathrm{120},\mathrm{360} \\ $$

Commented by liki last updated on 24/Nov/19

..thanks sir,,can you assist me simple logic   of get third no,why did you take 2^3  ??

$$..{thanks}\:{sir},,{can}\:{you}\:{assist}\:{me}\:{simple}\:{logic}\: \\ $$$${of}\:{get}\:{third}\:{no},{why}\:{did}\:{you}\:{take}\:\mathrm{2}^{\mathrm{3}} \:?? \\ $$

Commented by mr W last updated on 24/Nov/19

y=2^3 ×3^(1..2) ×5^(0..1)   i.e.  y_1 =2^3 ×3^1 ×5^0 =24  y_2 =2^3 ×3^2 ×5^0 =72  y_3 =2^3 ×3^1 ×5^1 =120  y_4 =2^3 ×3^2 ×5^1 =360

$${y}=\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{1}..\mathrm{2}} ×\mathrm{5}^{\mathrm{0}..\mathrm{1}} \\ $$$${i}.{e}. \\ $$$${y}_{\mathrm{1}} =\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{1}} ×\mathrm{5}^{\mathrm{0}} =\mathrm{24} \\ $$$${y}_{\mathrm{2}} =\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{2}} ×\mathrm{5}^{\mathrm{0}} =\mathrm{72} \\ $$$${y}_{\mathrm{3}} =\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{1}} ×\mathrm{5}^{\mathrm{1}} =\mathrm{120} \\ $$$${y}_{\mathrm{4}} =\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{2}} ×\mathrm{5}^{\mathrm{1}} =\mathrm{360} \\ $$

Commented by liki last updated on 24/Nov/19

...plz mr w,tell me the logic of take 2^3 ..

$$...{plz}\:{mr}\:{w},{tell}\:{me}\:{the}\:{logic}\:{of}\:{take}\:\mathrm{2}^{\mathrm{3}} .. \\ $$

Commented by mr W last updated on 24/Nov/19

in 360 we have 2^3 , but in 18 and 60 we  have max. 2^2 , therefore in y we must  have at least 2^3 .

$${in}\:\mathrm{360}\:{we}\:{have}\:\mathrm{2}^{\mathrm{3}} ,\:{but}\:{in}\:\mathrm{18}\:{and}\:\mathrm{60}\:{we} \\ $$$${have}\:{max}.\:\mathrm{2}^{\mathrm{2}} ,\:{therefore}\:{in}\:{y}\:{we}\:{must} \\ $$$${have}\:{at}\:{least}\:\mathrm{2}^{\mathrm{3}} . \\ $$

Commented by liki last updated on 24/Nov/19

..Thank you so much sir be blesed

$$..{Thank}\:{you}\:{so}\:{much}\:{sir}\:{be}\:{blesed} \\ $$

Commented by liki last updated on 24/Nov/19

..so it mean to get; y_1 =2^3 ×3^1 =24                                           y_2 =2^3 ×3^2 =72                                            y_3 =?                                            y_4 =?  ..how to get y_3  & y_4

$$..{so}\:{it}\:{mean}\:{to}\:{get};\:{y}_{\mathrm{1}} =\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{1}} =\mathrm{24} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}_{\mathrm{2}} =\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{2}} =\mathrm{72} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}_{\mathrm{3}} =? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}_{\mathrm{4}} =? \\ $$$$..{how}\:{to}\:{get}\:{y}_{\mathrm{3}} \:\&\:{y}_{\mathrm{4}} \\ $$$$ \\ $$

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