Find the LCM and HCF of the following product of the two numbers
(i) 26 and 91
(ii) 510 and 92

Given:

Given pairs of integers is

(i) 26 and 91
(ii) 510 and 92

To do:

Here we have to find the LCM and HCF of the given pairs of integers.

Solution: 

(i) Calculating LCM and HCF using prime factorization method:

Writing the numbers as a product of their prime factors:

Prime factorisation of 26:

• $2\ \times\ 13\ =\ 2^1\ \times\ 13^1$

Prime factorisation of 91:

• $7\ \times\ 13\ =\ 7^1\ \times\ 13^1$

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

$2^1\ \times\ 13^1\ \times\ 7^1\ =\ 182$

LCM(26, 91) $=$ 182

Multiplying all common prime factors: 

$13^1\ =\ 13$

HCF(26, 91) $=$ 13

 (ii) Calculating LCM and HCF using prime factorization method:

Writing the numbers as a product of their prime factors:

Prime factorisation of 510:

• $2\ \times\ 3\ \times\ 5\ \times\ 17\ =\ 2^1\ \times\ 3^1\ \times\ 5^1\ \times\ 17^1$

Prime factorisation of 92:

• $2\ \times\ 2\ \times\ 23\ =\ 2^2\ \times\ 23^1$

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

$2^2\ \times\ 3^1\ \times\ 5^1\ \times\ 17^1\ \times\ 23^1\ =\ 23460$

LCM(510, 92) $=$ 23460

Multiplying all common prime factors: 

$2^1\ =\ 2$

HCF(510, 92) $=$ 2.