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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Question : The HCF and LCM of the two numbers are 21 and 84, respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is:
Option 1: 12
Option 2: 108
Option 3: 48
Option 4: 84
Question : Find the mean proportion between $(6+\sqrt{8})$ and $(3-\sqrt{2})$.
Option 1: $2 \sqrt{12}$
Option 3: $(6-\sqrt{8})$
Option 4: $\sqrt{15}-7$
Question : Two numbers are in the ratio of 6 : 5. If their HCF is 3, then what is the LCM of the two numbers?
Option 1: 64
Option 2: 110
Option 3: 90
Option 4: 80
Question : What is the ratio between the HCF and LCM of the numbers whose LCM is 48 and the product of the numbers is 384?
Option 1: 1 : 4
Option 2: 1 : 6
Option 3: 1 : 3
Option 4: 2 : 5
Question : The LCM of the two numbers is 4104 and the HCF is 9. If one of the numbers is 171, find the other.
Option 1: 218
Option 2: 215
Option 3: 220
Option 4: 216
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