# Difficult Number System Solved QuestionAptitude Discussion

 Q. The H.C.F of two numbers, each having three digits, is 17 and their L.C.M. is 714. The sum of the numbers will be:
 ✖ A. 119 ✔ B. 221 ✖ C. 237 ✖ D. 727

Solution:
Option(B) is correct

Let two numbers be $17x$ and $17y$ respectively, as $17$ is the HCF of these numbers.

Now, LCM of $17x$ and $17y$ is $17xy$

and, according to the question LCM of these two numbers, $=714$

$\Rightarrow 17xy = 714$

$\Rightarrow xy = \dfrac{714}{17}$

$\Rightarrow xy = 42 = 7 \times 6$

Now we have two possible scenarios,

either, $x =7$ and $y = 6$ ----(1)

or, $x =6$ and $y = 7$ ----(2)

In the first scenario, where $x =7$ and $y = 6$, numbers will be,

$17x = 17\times 7 = 119$

$17y = 17 \times 6 = 102.$

Or, in the second case where $x = 6$ and $y =7$, numbers will be $102$ and $119$.

Required sum would be,

$= 102 + 119$

$= 221.$