Find the LCM and HCF of the following pairs of integers and verify that LCM $\times$ HCF $=$ Product of the integers:
404 and 96

Given:

Given pair of integers is 404 and 96.

To do:

Here we have to find the LCM and HCF of the given pair of integers and then verify that LCM $\times$ HCF $=$ Product of the integers.

Solution: 

Calculating LCM and HCF using prime factorization method:

Writing the numbers as a product of their prime factors:

Prime factorisation of 404:

• $2\times2\times101=2^2\times101$

Prime factorisation of 96:

• $2\times2\times2\times2\times2\times3 =\ 2^5\ \times\ 3^1$

Multiplying the highest power of each prime number of these values together:

$2^5\ \times\ 3^1\ \times\ 101^1\ =\ 9696$

LCM(404, 96) $=$ 9696

Multiplying all common prime factors: 

$2^2\ =\ 4$

HCF(404, 96) $=$ 4

Now, verifying that LCM $\times$ HCF $=$ Product of the integers:

LCM $\times$ HCF $=$ Product of the integers

404 $\times$ 96 $=$ 9696 $\times$ 4

38784 $=$ 38784.

Hence verified.