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Q)

# If the LCM of $a$ and $18$ is 36 and HCF of $a$ and $18$ is $2$ then $a$=

$\begin{array}{1 1}(A) \; 2\\(B)\;3 \\(C)\;240\\(D)\;1 \end{array}$

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A)
$HCF \times LCM$ =Product of numbers
$a \times 18=36 \times 2$
$a=\large\frac{36 \times 2}{18}$
$\quad= 4$
$\large\frac{AB}{BC} =\frac{5}{12}$
$\qquad= \large\frac{h}{x+192}$
$\qquad= 5x+960$
$\qquad= 12\;h$
$\large\frac{AB}{PBD} =\frac{h}{x}$
$\qquad= \large\frac{3}{4}$
$4h=3x$
$5x+960=9x$
$x= 240\;m$