Question

The L.C.M of two numbers is $12$ times their H.C.F. The sum of the H.C.F. and L.C.M. is $403.$ If one of the numbers is $93,$ then what is the other number?

• A. $124$
• B. $128$
• C. $134$
• D. $138$

Answer 1

The correct option is A $124$

$L.C.M=12\times H.C.F$ and
$H.C.F+L.C.M=403$
$\Rightarrow H.C.F+12H.C.F=403$
$\Rightarrow 13H.C.F=403$
$\Rightarrow H.C.F=\frac{403}{13}=31$
$L.C.M.=12\times 31=372$

Given number $=93$
$\therefore$ Other number $=\frac{L\cdot C\cdot M\cdot \times H\cdot C\cdot F\cdot }{Givennumber}$
$=\frac{372\times 31}{93}=124$