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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Question : Determine the LCM of two numbers if their HCF is 12 and their ratio is 13 : 15.
Option 1: 1780
Option 2: 2450
Option 3: 1890
Option 4: 2340
Question : Two numbers are in the ratio of 4 : 3. The product of their HCF and LCM is 2700. The difference between the numbers is:
Option 1: 15
Option 2: 30
Option 3: 25
Option 4: 105
Question : The ratio of two numbers is 3 : 4 and their HCF is 5. Their LCM is:
Option 1: 10
Option 2: 60
Option 3: 15
Option 4: 12
Question : The product of two numbers is 20000. If their LCM is 800, then what is their HCF?
Option 1: 25
Option 3: 35
Option 4: 20
Question : The LCM of two numbers is five times their HCF. If the product of the two numbers is 20480, then find their HCF and LCM, respectively.
Option 1: 46 and 230
Option 2: 48 and 240
Option 3: 64 and 320
Option 4: 56 and 280
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