Question : If the LCM of two numbers a and b is 60 and their HCF is 15. Determine their mean proportion.
Option 1: 30
Option 2: 25
Option 3: 60
Option 4: 4
Correct Answer: 30
Solution :
The mean proportion of two numbers a and b is given by the square root of the product of a and b.
Given that the least common multiple (LCM) of a and b is 60 and their highest common factor (HCF) is 15.
⇒ a × b = LCM × HCF = 60 × 15 = 900
So, the mean proportion of a and b = $\sqrt{ab} = \sqrt{900} = 30$
Hence, the correct answer is 30.
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