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Question Number 176928 by Ar Brandon last updated on 28/Sep/22

$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{smallest}\mathrm{three}\mathrm{digit}\mathrm{number}$$$$\mathrm{divisible}\mathrm{by}\frac{2}{3},\frac{7}{9},\frac{4}{13}\mathrm{without}\mathrm{a}\mathrm{remainder}?$$

Answered by mr W last updated on 28/Sep/22

$$N=\frac{2}{3}a=\frac{7}{9}b=\frac{4}{13}c$$$$a=3p,b=9q,c=13r$$$$N=2p=7q=4r$$$$\Rightarrow N=28k$$$$for3digitnumbers{N}_{min}=28\times 4=112$$

Commented by Ar Brandon last updated on 28/Sep/22

Thanks

Commented by Tawa11 last updated on 28/Sep/22

$$\mathrm{Great}\mathrm{sirs}.$$

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