 # LCM & HCF of 3 numbers - Prime Factorization

Ex 1.2 Q3. CBSE 10th Maths NCERT exercise solution

#### Question 3: Find the LCM and HCF of the following integers by applying the prime factorisation method.

i. 12, 15 and 21
ii. 17, 23 and 29
iii. 8, 9 and 25

##### i. 12, 15 and 21

Step 1: Prime factorize the numbers
12 = 22 × 3
15 = 3 × 5
21 = 3 × 7

Step 2: Compute HCF: HCF = Product of the lowest powers of common primes in the 3 numbers.
HCF (12, 15, 21) = 3

Step 3: Compute LCM: LCM = Product of the highest powers of all the primes in the 3 numbers.
LCM (12, 15, 21) = 22 × 3 × 5 × 7 = 420

##### ii. 17, 23 and 29

Step 1: Prime factorize the numbers
All 3 are prime numbers. So, there is nothing to be done in step 1.

Step 2: Compute HCF: HCF = Product of the lowest powers of common primes in the 3 numbers.
∴ HCF (17, 23, 29) = 1
Note: If all the given numbers are prime, they will have no common factor other than 1. So, HCF will be 1 for two or more prime numbers.

Step 3: Compute LCM: LCM = Product of the highest powers of all the primes in the 3 numbers.
LCM (17, 23, 29) = 17 × 23 × 29 = 11339
Note: If the given numbers are all prime, their LCM will be the product of the numbers.

##### iii. 8, 9 and 25

Step 1: Prime factorize the numbers
8 = 23
9 = 32
25 = 52

Step 2: Compute HCF: HCF = Product of the lowest powers of common primes in the 3 numbers.
No prime factor common to the 3 numbers.
∴ HCF (8, 9, 25) = 1

Step 3: Compute LCM: LCM = Product of the highest powers of all the primes in the 3 numbers.
LCM (8, 9, 25) = 23 × 32 × 52 = 8 × 9 × 25 = 1800