Question: Using Prime Factorization, Find the HCF and LCM of 396 and 1080


Question: How to Find The HCF and LCM of 396 and 1080 by Using Prime Factorization?

HCF (Highest Common Factor) of 396 and 1080 is the largest possible number which divides both 396 and 1080 exactly. Least Common Multiple of 396 and 1080 is the smallest number which is exactly divisible by 396 and 1080

Answer: HCF of 396 and 1080 is 36, LCM of 396 and 1080 is 11880

We will explain the prime factorization method to find the HCF and the LCM of 396 and 1080.

Explanation:

HCF of 396 and 1080 by Prime Factorization Method

Prime Factorization of 396 = 2 × 2 × 3 × 3 × 11 

Prime Factorization of 1080 =  2 × 2 × 2 × 3 × 3 × 3 × 5

We see that 2 × 2 × 3 × 3  appears in bot prime factorization

Therefore HCF of 396 and 1080 = 2 × 2 × 3 × 3 = 36 

Answer: HCF of 396 and 1080 is 36

Now, let's find out the LCM of 396 and 1080

LCM of 396 and 1080 by Prime Factorization Method

Prime Factorization of 396 =  2 × 2 × 3 × 3 × 11 = 22 × 32 × 11

Prime Factorization of 1080 =   2 × 2 × 2 × 3 × 3 × 3 × 5 =  23 × 33 × 5

LCM is the product of all prime factors the greatest number of times they occur in either number.

LCM(396, 1080) = 23 × 33 × 11 × 5

= 8 × 27 × 11 × 5

= 11,880    

Therefore, HCF of 396 and 1080 is 36 and LCM of 396 and 1080 is 11880.