HCF and LCM of two numbers are 11 and 385 .If one number lies between 75 and 125 then that number isa)123b)73c)77d)154e)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Product of the two number = 11a×11b = 4235
11a×11ab = 4235/121 = 35
35 = 7 × 5 (co prime)
77 × 11 = 77

Answer

Let the Nos be X and y.
then it is quite clear that,
11x*11y=11*385. (X*Y=HCF*LCM)

•. XY=35 and X and y should be. co-prime
therefore 5*7=x*y would be the required
pair

hence first no is 55 and second no is 77
therefore 77 is the absolute. answer for this question

Answer

HCF and LCM are important concepts in number theory. HCF stands for Highest Common Factor, which is the largest number that divides two numbers evenly. LCM stands for Lowest Common Multiple, which is the smallest number that is a multiple of two numbers.

Given that the HCF is 11 and the LCM is 385, we can use these values to find the two numbers.

To find the two numbers, we can use the formula:

HCF x LCM = Product of the two numbers

So, 11 x 385 = Product of the two numbers

The product of the two numbers is 4235.

Now, we need to find the two numbers that have a product of 4235 and one of them lies between 75 and 125.

Let's consider the factors of 4235:

1 x 4235 = 4235
5 x 847 = 4235
11 x 385 = 4235
35 x 121 = 4235
55 x 77 = 4235

Out of these pairs, only one number lies between 75 and 125, which is 77. Therefore, the other number must be 55.

So, the two numbers are 77 and 55.

Now, let's verify if the HCF and LCM of these two numbers are indeed 11 and 385.

The HCF of 77 and 55 is 11.

To find the LCM, we can use the formula:

LCM = (Product of the two numbers) / HCF

LCM = (77 x 55) / 11
LCM = 4235 / 11
LCM = 385

Therefore, the HCF and LCM of 77 and 55 are indeed 11 and 385, respectively.

Hence, the number that lies between 75 and 125 is 77, which is option C.

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