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Find the LCM and HCF of the following integers by applying the prime factorization method:
17, 23 and 29
Given: 17, 23 and 29.
To find: Here we have to find the LCM and HCF of the given integers by applying the prime factorization method.
Solution:
Calculating LCM and HCF using prime factorization method:
Writing the numbers as a product of their prime factors:
Prime factorisation of 17:
- $17\ =\ 17^1$
Prime factorisation of 23:
- $23\ =\ 23^1$
Prime factorisation of 29:
- $29\ =\ 29^1$
Multiplying the highest power of each prime number these values together:
$17^1\ \times\ 23^1\ \times\ 29^1\ =\ 11339$
LCM(17, 23, 29) $=$ 11339
Multiplying all common prime factors:
There is no common prime factor. So,
HCF(17, 23, 29) $=$ 1
So, the LCM and HCF of 17, 23 and 29 are 11339 and 1 respectively.
Updated on: 10-Oct-2022
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