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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