Find the HCF of 96 and 404 by prime factorization and use it to find the LCM

The HCF (Highest Common Factor) of two numbers is the largest possible number which divides the two numbers exactly without any remainder.

Answer: The HCF of 96 and 404 is 4, and the LCM of 96 and 404 is 9696

We will find the HCF of 96 and 404 by using the prime factorization method, and then by using the formula we will calculate their LCM.

Explanation:

Represent 96 and 404 as a product of its prime factors.

The Prime factorization  of 96 is 2 × 2 × 2 × 2 × 2 × 3 

Prime factorization of 404 is 2 × 2 × 101

HCF is the product of the factors that are common to each of the given numbers.

Since the common factors are 2 and 2, the HCF of 96 and 404 is 4

We will use the formula to calculate the LCM of two numbers (a, b):

LCM (a, b) = (a × b) / HCF (a, b)

HCF (a, b) is the highest common factor of a and b.

Using the formula,

LCM (96, 404) = (96 × 404) / HCF (96, 404)

By substituting the values,

= (96 × 404) / 4

= 96 × 101

= 9696

Therefore, the HCF of 96 and 404 is 4, and the LCM of 96 and 404 is 9696