Question Number 176928 by Ar Brandon last updated on 28/Sep/22
$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{three}\:\mathrm{digit}\:\mathrm{number} \\ $$$$\mathrm{divisible}\:\mathrm{by}\:\frac{\mathrm{2}}{\mathrm{3}},\:\frac{\mathrm{7}}{\mathrm{9}},\:\frac{\mathrm{4}}{\mathrm{13}}\:\mathrm{without}\:\mathrm{a}\:\mathrm{remainder}\:? \\ $$
Answered by mr W last updated on 28/Sep/22
$${N}=\frac{\mathrm{2}}{\mathrm{3}}{a}=\frac{\mathrm{7}}{\mathrm{9}}{b}=\frac{\mathrm{4}}{\mathrm{13}}{c} \\ $$$${a}=\mathrm{3}{p},\:{b}=\mathrm{9}{q},\:{c}=\mathrm{13}{r} \\ $$$${N}=\mathrm{2}{p}=\mathrm{7}{q}=\mathrm{4}{r} \\ $$$$\Rightarrow{N}=\mathrm{28}{k} \\ $$$${for}\:\mathrm{3}\:{digit}\:{numbers}\:{N}_{{min}} =\mathrm{28}×\mathrm{4}=\mathrm{112} \\ $$
Commented by Ar Brandon last updated on 28/Sep/22
Thanks
Commented by Tawa11 last updated on 28/Sep/22
$$\mathrm{Great}\:\mathrm{sirs}. \\ $$