Question Number 202830 by dimentri last updated on 04/Jan/24
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Answered by mr W last updated on 04/Jan/24
$${lcm}\left(\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{9}\right)=\mathrm{5}×\mathrm{7}×\mathrm{9}=\mathrm{315} \\ $$$$\Rightarrow{n}=\mathrm{315}{k}−\mathrm{1} \\ $$$${n}_{{min}} =\mathrm{314} \\ $$
Commented by dimentri last updated on 04/Jan/24
$$\mathrm{why}\:\mathrm{n}=\mathrm{315k}−\mathrm{1}\: \\ $$$$\:\mathrm{sir}\: \\ $$
Commented by mr W last updated on 04/Jan/24
$${the}\:{question}\:{is}\:{the}\:{same}\:{as} \\ $$$${n}+\mathrm{1}=\mathrm{0}\:\left({mod}\:\mathrm{3}\right) \\ $$$${n}+\mathrm{1}=\mathrm{0}\:\left({mod}\:\mathrm{5}\right) \\ $$$${n}+\mathrm{1}=\mathrm{0}\:\left({mod}\:\mathrm{7}\right) \\ $$$${n}+\mathrm{1}=\mathrm{0}\:\left({mod}\:\mathrm{9}\right) \\ $$$$\Rightarrow{n}+\mathrm{1}=\mathrm{315}{k} \\ $$$$\Rightarrow{n}=\mathrm{315}{k}−\mathrm{1} \\ $$