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Find the LCM and HCF of the following integers by applying the prime factorization method:
12, 15 and 21
Given: 12, 15 and 21.
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 12:
- $2\ \times\ 2\ \times\ 3\ =\ 2^2\ \times\ 3^1$
Prime factorisation of 15:
- $3\ \times\ 5\ =\ 3^1\ \times\ 5^1$
Prime factorisation of 21:
- $3\ \times\ 7\ =\ 3^1\ \times\ 7^1$
Multiplying the highest power of each prime number these values together:
$2^2\ \times\ 3^1\ \times\ 5^1\ \times\ 7^1\ =\ 420$
LCM(12, 15, 21) $=$ 420
Multiplying all common prime factors:
$3^1\ =\ 3$
HCF(12, 15, 21) $=$ 3
So, the LCM and HCF of 12, 15 and 21 are 420 and 3 respectively.
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