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Question Number 50209 by mondodotto@gmail.com last updated on 14/Dec/18

$$\mathbf{The}\mathbf{gcf}\mathbf{and}\mathbf{lcm}\mathbf{of}\mathbf{three}\mathbf{numbers}$$$$\mathbf{are}2\mathbf{and}1200\mathbf{respectively}.$$$$\mathbf{if}\mathbf{the}\mathbf{two}\mathbf{numbers}\mathbf{are}16\mathbf{and}24,$$$$\mathbf{find}\mathbf{the}\mathbf{third}\mathbf{number}$$

Answered by mr W last updated on 14/Dec/18

$${let}^{\prime }ssaythethirdnumberisN$$$$gcf(N,16,24)=2$$$$since16=2^{4}and24=2^3\times 3$$$$\Rightarrow N=2^1\mathrm{\Pi }{p}^{i}withp⩾3$$$$lcm(N,16,24)=1200$$$$since1200=2^4\times 3\times 5^2$$$$\Rightarrow N=2^1\times 5^2=50or{2}^1\times 3\times 5^2=150$$$$i.e.thethirdnumberis50or150.$$

Commented by mr W last updated on 15/Dec/18

$$MJSsirshouldcheck.heisexpertfor$$$$suchquestions.$$

Commented by mondodotto@gmail.com last updated on 15/Dec/18

$$\mathrm{oky}\mathrm{thanks}$$

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