The LCM of two numbers is 12 times their HCF. The sum of HCF and LCM is 403. If one number is 93, find the other = ?

$$\eqalign{ & {\text{Let HCF be }}h{\text{ and LCM be }}l \cr & {\text{Then }}l = {\text{ }}12h{\text{ and}} \cr & {\text{ }}l + h{\text{ }} = {\text{ }}403 \cr & \therefore 12h + h = 403{\text{ or }}h = {\text{ }}31 \cr & {\text{So }}l{\text{ = }}\left( {403 - 31} \right) = 372 \cr & {\text{Hence other number}} \cr & {\text{ = }}\left( {\frac{{31 \times 372}}{{93}}} \right) = 124 \cr} $$