Let the numbers be 17a and 17b. Then, 17a × 17b = 17 × 714 ⇒ ab = 42. Now, co-primes with product 42 are (1, 42), (2, 21), (3, 14) and (6, 7). So, the numbers are (17 × 1, 17 × 42), (17 × 2, 17 × 21), (17 × 3, 17 × 14) and (17 × 6, 17 × 7). Since both the numbers are 3-digit numbers, the suitable pair is (17 × 6, 17 × 7), i.e., (102, 119). $\therefore$ Required sum = 102 + 119 = 221.
Explanation as extracted from the printed page; notation may be imperfect.