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Question Number 94025 by Rasheed.Sindhi last updated on 16/May/20

$$\mathrm{LCM}(a,\frac{3}{5}a)=3a\wedge \mathrm{HCF}(a,\frac{3}{5}a)=\frac{1}{5}a$$$$a=?$$

Commented by som(math1967) last updated on 16/May/20

$$\mathrm{sir},\mathrm{if}\mathrm{a}=5\mathrm{then}\mathrm{L}.\mathrm{C}.\mathrm{M}=15$$$$\mathrm{i}.\mathrm{e}3\times 5$$$$\mathrm{HCF}=1\mathrm{i}.\mathrm{e}\frac{1}{5}\times 5=1$$$$\mathrm{also}\mathrm{if}\mathrm{a}=1$$$$\mathrm{LCM}=3\mathrm{i}.\mathrm{e}3\times 1$$$$\mathrm{HCF}=\frac{1}{5}$$$$\mathrm{also}\mathrm{valid}\mathrm{when}\mathrm{a}\in \mathrm{R}$$$$\mathrm{so}\mathrm{I}\mathrm{think}\mathrm{a}\mathrm{is}\mathrm{any}\mathrm{real}\mathrm{number}$$

Commented by Rasheed.Sindhi last updated on 16/May/20

$$\mathcal{T}han\mathcal{X}Sir!$$

Commented by Rasheed.Sindhi last updated on 16/May/20

$$Ifa\in \mathbb{Z}?$$

Commented by som(math1967) last updated on 17/May/20

$$\mathrm{If}\mathrm{a}=-3[-3\in \mathrm{Z}]$$$$\therefore \mathrm{LCM}\mathrm{of}-3,\frac{-9}{5}\mathrm{is}-9$$$$\mathrm{i}.\mathrm{e}3\times -3\mathrm{HCF}\mathrm{is}\frac{-3}{5}\mathrm{i}.\mathrm{e}-3\times \frac{1}{5}$$$$\therefore \mathrm{true}\mathrm{if}\mathrm{a}\in \mathrm{Z}$$$$\mathrm{also}\mathrm{we}\mathrm{know}\mathrm{Z}\in \mathrm{R}$$$$$$

Commented by Rasheed.Sindhi last updated on 17/May/20

$$\mathcal{T}hanksagainSir!$$$$ActullyImeanta,\frac{3}{5}a\mathrm{\&}\frac{1}{5}aall$$$$belongingtointegers!$$$$SorrythatI{didn}^{\prime }tmadeitclear!$$

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