Question

Find the HCF and LCM of 24 and 36 by prime factorization method.

Answer 1

Hint: Prime factorization uses prime numbers only. We write the number as a product of the prime numbers and then we proceed to find the LCM and HCF. These are found separately.

Complete step-by-step answer:
Given the numbers are 24 and 36.
These are to be written in the form of a product of prime numbers. so, we can write,
 \[24 = 2 \times 2 \times 2 \times 3\]
 \[36 = 2 \times 2 \times 3 \times 3\]
Now we will proceed towards finding the LCM and HCF
HCF:
The common numbers in the product pattern are \[2 \times 2 \times 3\] . Thus the HCF is 12.

LCM:
Now to find the LCM we will use the uncommon numbers also.
Thus we have \[2 \times 3\] as the uncommon factors. Thus the LCM will be,
 \[12 \times 2 \times 3 = 72\]
So, the HCF is 12 and LCM is 72.

Note: Note that factors and multiples are two different concepts. To cross verify the answer we will use the formula that the product of LCM and HCF of two numbers is equal to the product of two numbers.
Thus \[24 \times 36 = 864\] and \[12 \times 72 = 864\] . Thus the LCM and HCF are correct.