The LCM of two numbers is 1200 .Which of following van not be their HCFa)600b)500c)400d)200Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Answer

LCM=1200,
HCF=?,
if LCM is 1200 it means that the HCF is a factor of LCM .
or, from the following options all no.s can divide 1200 expect 500.
Hence, it can't be HCF

Answer

Finding HCF and LCM of two numbers is a fundamental concept in mathematics. Let's understand the concept and solve the given problem.

Concept of HCF and LCM

HCF (Highest Common Factor) is the greatest common factor that divides two or more numbers exactly. For example, the HCF of 12 and 18 is 6 because 6 is the highest common factor that divides both 12 and 18.

LCM (Least Common Multiple) is the smallest common multiple of two or more numbers. For example, the LCM of 4 and 6 is 12 because 12 is the smallest number that is a multiple of both 4 and 6.

To find the HCF and LCM of two numbers, we can use the prime factorization method. We express both numbers as a product of prime factors and then HCF is the product of common prime factors with the least power, and LCM is the product of all prime factors with the highest power.

Given Problem

The LCM of two numbers is 1200. We need to find which of the following cannot be their HCF - 600, 500, 400, or 200.

Solution

Let's assume the two numbers are a and b. Then, we can write:

LCM(a, b) = 1200

We need to find the HCF of a and b that cannot be any of the given options.

We know that HCF x LCM = a x b

HCF(a, b) x 1200 = a x b

HCF(a, b) = (a x b) / 1200

Since HCF is a factor of a and b, we can assume that a = HCF x p and b = HCF x q, where p and q are co-prime (i.e., they have no common factors other than 1).

Substituting the values of a and b in the above equation, we get:

HCF(a, b) = (HCF x p x HCF x q) / 1200

HCF(a, b) = (HCF^2 x p x q) / 1200

HCF(a, b) = (HCF/12)^2 x p x q

This shows that HCF/12 is a factor of HCF(a, b). Therefore, HCF cannot be 500 because 500/12 is not a factor of any of the given options.

Let's check the other options:

- HCF = 600 -> HCF/12 = 50 -> 50 is a factor of 400, so it can be their HCF.
- HCF = 400 -> HCF/12 = 33.33 (not an integer) -> it cannot be their HCF.
- HCF = 200 -> HCF/12 = 16.67 (not an integer) -> it cannot be their HCF.

Therefore, the correct answer is option B - 500 cannot be their HCF.

Conclusion

In this problem, we used the concept of HCF and LCM to find which of the given options cannot be the HCF of two numbers whose LCM is 1200. We used the prime factorization method and the formula HCF x LCM = a x b to derive the solution.

Answer

500 kyuki LCM HCF ka multiple hota hai

Answer

It's common

because 500 is not a factor of 1200 .

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