Find the LCM and HCF of the following integers by applying the prime factorization method:
24, 15 and 36

Given: 24, 15 and 36.

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 24:

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

Prime factorisation of 15:

• $3\ \times\ 5\ =\ 3^1\ \times\ 5^1$

Prime factorisation of 36:

• $2\ \times\ 2\ \times\ 3\ \times\ 3\ =\ 2^2\ \times\ 3^2$

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

$2^3\ \times\ 3^2\ \times\ 5^1\ =\ 360$

LCM(24, 15, 36)  $=$  360

Multiplying all common prime factors: 

$3^1\ =\ 3$

HCF(24, 15, 36)  $=$  3

So, the LCM and HCF of 24, 15 and 36 are 360 and 3 respectively.