Question

If the H.C.F. of two numbers (each greater than $13$) be $13$ and the L.C.M. be $273,$ then what will be the sum of the numbers?

• A. $288$
• B. $290$
• C. $130$
• D. $286$

Answer 1

The correct option is C $130$

Let the numbers be $13a$ and $13b$ where $a$ and $b$ are co-primes.
L.C.M. of $13$ $\times$ $a$ and $13$ $\times$ $b=$ $13\times a\times b$
$=13ab.$
Given $13ab=273$ $\Rightarrow$ $ab=21.$
$\therefore$ The set of co-primes satisfying
$ab=21$ is $(3,7)$
$\therefore$ The numbers are $13\times 3=39$ and
$13\times 7=91$
Hence, their sum $=39+91=130.$