Explanation:

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
⇒17xy=714
⇒xy=714/17
⇒xy=42=7×6
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=17×7=119
17y=17×6=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