Lcm And Hcf

Given polynomials: Using the polynomial division method, we find that the remainder is:
Thus, the HCF of both polynomials is:
Thus, the correct answer is .

We find the HCF(65, 117) using the Euclidean Algorithm:
Thus, HCF(65, 117) = 13. Now, express 13 as a linear combination: Since 52 = 117 - 65 \times 1, substitute:
Thus, comparing with , we get:
Thus, the correct answer is 2.

We find the prime factorization of each number: - 90 = - 60 = - 75 = - 35 = Taking the highest powers of all prime factors: Step-by-step multiplication:
Thus, the LCM is 6300.

We find the prime factorization of each number:
- 54 =
- 288 =
- 360 =
Now, taking the **minimum power** of each common factor:

Thus, the HCF is 18.

Using the relation: