Question : If the LCM and the HCF of two numbers are 12 and 2 respectively, then find the mean proportional of these numbers.
Option 1: $2 \sqrt{6}$
Option 2: $\sqrt{14}$
Option 3: $2$
Option 4: $\sqrt{6}$
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Correct Answer: $2 \sqrt{6}$
Solution :
We know that LCM × HCF = Product of two numbers
Now Mean proportion = $\sqrt{\text{Product of two numbers}}$
Given:
LCM = 12
HCF = 2
$\therefore$ Product of two numbers $= 12 \times 2 = 24$
Mean proportion $=\sqrt{24} = \sqrt{4\times 6}=2\sqrt{6}$
Hence the correct answer is $2\sqrt{6}$.
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