Question : The LCM and HCF of the two numbers are 1105 and 5. If the LCM is 17 times the first number, then find the two numbers.
Option 1: 65 and 85
Option 2: 55 and 85
Option 3: 65 and 75
Option 4: 60 and 80
Correct Answer: 65 and 85
Solution : LCM = 1105 HCF = 5 Let the first number be $x$ and the second number be $y$. $17 x= 1105$ $⇒x = \frac{1105}{17} = 65$ We know, LCM × HCF = $x × y$ $⇒1105 × 5 = 65 × y$ $\therefore y = \frac{1105 × 5 }{65}= 85$ Hence, the correct answer is 65 and 85.
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