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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.