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Question Number 158711 by HongKing last updated on 07/Nov/21

Commented by Rasheed.Sindhi last updated on 08/Nov/21

$$1000000$$

Commented by HongKing last updated on 08/Nov/21

$$\mathrm{how}\mathrm{my}\mathrm{dear}\mathbf{S}\mathrm{ir}...$$

Answered by ajfour last updated on 08/Nov/21

$$N=n^2=m^3=20k=2^2\times 5\times k_{min}$$$$primescannotbecompensated$$$$N=2^6\times 5^6={10}^6=1million$$

Commented by HongKing last updated on 08/Nov/21

$$\mathrm{very}\mathrm{nice}\mathrm{dear}\mathrm{Ser}\mathrm{thank}\mathrm{you}$$

Answered by Rasheed.Sindhi last updated on 08/Nov/21

$$Requirednumber:$$$$A=2^{m⩾2}.5^{n⩾1}[\because 20(=2^2.5^1)\mid A]..........\left(\mathrm{i}\right)$$$$A=2^{\mathrm{k}.\mathrm{LCM}(2,3)}.5^{\mathrm{k}.\mathrm{LCM}(2,3)}.............\left(\mathrm{ii}\right)$$$$[\because Aissametimeperfectsquare$$$$\left({◻}^2\right)\mathrm{\&}perfectcube\left({△}^3\right)]$$$$\left(\mathrm{i}\right)\mathrm{\&}\left(\mathrm{ii}\right):A=2^{1\times 6}.5^{1\times 6}=1000000$$$$[Aistheleastsuchnumberso\mathrm{k}=1]$$

Commented by HongKing last updated on 08/Nov/21

$$\mathrm{very}\mathrm{nice}\mathrm{dear}\mathrm{Ser}\mathrm{thank}\mathrm{you}$$

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