- I and III together
- All the statements
- I and II together
- I and either II or III
- Any two statements together
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Option 2 : All the statements
Since HCF and LCM are 17 and 714 (Statement I and III)
Let two numbers be 17x and 17y respectively, as 17 is the HCF of these numbers
Now, LCM of 17x and 17y is 17xy
According to the question LCM of these two numbers = 714
⇒ 17xy = 714
⇒ xy = 714/17
⇒ xy = 42 = 7 × 6
Now as numbers are of 3 digits (Statement II)
In this scenario, where x = 7 and y = 6,
Numbers will be,
17x = 17 × 7 = 119
17y = 17 × 6 = 102
Required sum would be,
⇒ 102 + 119
⇒ 221
Hence All the statements are necessary to answer the question
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