Question

explain fundamental arithematic theorem by using it find lcm is hcf of 12 and 18

Answer 1

hcf of 18 and 12 is 6

Answer 2

$\huge{\underline{\underline{\sf{Fundamental\:Theorem\:Of\:Arithematic}}}}$

• The theorem states that every composite number can be written as a product of primes, and this factorization is unique apart from the order in which the prime factors occur.

This method is also called the prime factorization method.

                                                                           

                                                                                 

Solving the second part of the question,

Using this theorem let us find the LCM and HCF of the given numbers, 12 & 18.

HCF = Highest common factor.

Let us write the multiples of 12 & 18.

              12  →  1, 2, 3, 4, 6, 12.

              18  → 1, 2, 3, 6, 9, 18.

We can see that 1, 2, 3 & 6 are the factors which both the given numbers have. But, to find the HCF we would need the highest factor, which is 6.

So, the HCF of 12 & 18 = 6.

For finding the LCM, have a look at the attachment.

We can see that the LCM of 12 & 18 = 36.