Question Number 135990 by zakirullah last updated on 17/Mar/21
$$\:\:\:\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{lowest}}\:\boldsymbol{{number}}\:\boldsymbol{{between}}\:\mathrm{200}\:\boldsymbol{{and}}\:\mathrm{500}\:\boldsymbol{{which}} \\ $$$$\:\:\:\:\:\boldsymbol{{leaves}}\:\boldsymbol{{a}}\:\boldsymbol{{remainder}}\:\boldsymbol{{of}}\:\mathrm{3}\:\boldsymbol{{in}}\:\boldsymbol{{each}}\:\boldsymbol{{case}} \\ $$$$\:\:\:\:\boldsymbol{{which}}\:\boldsymbol{{will}}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{8}\:,\:\mathrm{10},\:\mathrm{12}\:\boldsymbol{{and}}\:\mathrm{30}? \\ $$
Answered by Olaf last updated on 17/Mar/21
$$\mathrm{N}\:=\:\mathrm{8}{k}+\mathrm{3}\:=\:\mathrm{10}{l}+\mathrm{3}\:=\:\mathrm{12}{m}+\mathrm{3}\:=\:\mathrm{30}{n}+\mathrm{3} \\ $$$$\mathrm{200}\leqslant\mathrm{N}\leqslant\mathrm{500}\:\Rightarrow\:\mathrm{7}\leqslant{n}\leqslant\mathrm{16} \\ $$$$ \\ $$$$\mathrm{12}{m}+\mathrm{3}\:=\:\mathrm{30}{n}+\mathrm{3}\:\Rightarrow\:\mathrm{5}{n}\:=\:\mathrm{2}{m} \\ $$$$\Rightarrow\:{n}\in\left\{\mathrm{8},\:\mathrm{10},\mathrm{12},\:\mathrm{14},\:\mathrm{16}\right\} \\ $$$$ \\ $$$$\mathrm{N}_{{min}} \:=\:\mathrm{30}.\mathrm{8}+\mathrm{3}\:=\:\mathrm{243}\:=\:\mathrm{12}.\mathrm{20}+\mathrm{3}\:=\:\mathrm{10}.\mathrm{24}+\mathrm{3}\:=\:\mathrm{8}.\mathrm{30}+\mathrm{3} \\ $$
Commented by zakirullah last updated on 18/Mar/21
$$\:\:\:\:\boldsymbol{{you}}\:\boldsymbol{{are}}\:\boldsymbol{{right}}\:\boldsymbol{{dear}}\:\boldsymbol{{sir}}!\:\boldsymbol{{but}}\:\boldsymbol{{how}}\:\boldsymbol{{can}}\:\boldsymbol{{i}}\:\boldsymbol{{understand}} \\ $$$$\:\:\:\:\boldsymbol{{children}}\:\boldsymbol{{of}}\:\boldsymbol{{class}}\:\mathrm{6}\boldsymbol{{th}}. \\ $$$$\:\:\:\:\boldsymbol{{sir}}\:\boldsymbol{{can}}\:\boldsymbol{{you}}\:\boldsymbol{{do}}\:\boldsymbol{{this}}\:\boldsymbol{{on}}\:\boldsymbol{{simple}}\:\boldsymbol{{method}}? \\ $$
Answered by mr W last updated on 18/Mar/21
$${LCM}\:{from}\:\mathrm{8}\:{and}\:\mathrm{12}\:{is}\:\mathrm{24}. \\ $$$${LCM}\:{from}\:\mathrm{24}\:{and}\:\mathrm{30}\:{is}\:\mathrm{120}. \\ $$$${such}\:{a}\:{number}\:{is}\:{a}\:{multiple}\:{of}\:\mathrm{120} \\ $$$${plus}\:\mathrm{3},\:{i}.{e}.\:\mathrm{123},\:\mathrm{243},\:\mathrm{363}\:{etc}. \\ $$$${smallest}\:{between}\:\mathrm{200}\:{and}\:\mathrm{500}\:{is}\:\mathrm{243}. \\ $$$${largest}\:{between}\:\mathrm{200}\:{and}\:\mathrm{500}\:{is}\:\mathrm{483}. \\ $$
Commented by otchereabdullai@gmail.com last updated on 18/Mar/21
$$\mathrm{powerful}! \\ $$
Commented by zakirullah last updated on 18/Mar/21
$$\mathrm{ok}\:\mathrm{welldon} \\ $$