Question

3. Find the LCM and HCF of the following integers by applying the prime factorisation
method.
( 12, 15 and 21 (ii) 17,23 and 29
(iii) 8,9 and 25​

Answer 1

Answer:

Let's look into the prime factorization method to calculate the HCF and LCM

Explanation:

Follow the steps mentioned below to find the LCM of the given integer.

Step 1: Write down the prime factorization of each integer.

Step 2: Write the prime factorization of each integer in exponential form and select the highest power of all the factors that occur in any of these numbers.

Step 3: Find the product of factors found in step 2.

 

Follow the steps mentioned below to find the HCF of the given integer.

Step 1: Write down the prime factorization of each integer.

Step 2: Write the common factors of each integer.

Step 3: Find the product of factors found in step 2.

(1)

Prime factorization of 12 : 2 × 2 × 3 = 22 × 3

Prime factorization of 15 : 3 × 5

Prime factorization of 21 : 3 × 7

LCM of 12, 15, and 21 is given as:

LCM(12, 15, 21) = 22 × 3 × 5 × 7 = 4 × 3 × 5 × 7 = 420

HCF of 12, 15, and 21 is given as:

Common factors of the three numbers are: 3

HCF(12, 15, 21) = 3

(2)

Prime factorization of 17 : 17

Prime factorization of 23 : 23

Prime factorization of 29 : 29

LCM of 17, 23, and 29 is given as:

LCM(17, 23, 29) = 17 × 23 × 29 = 11339

HCF of 17, 23, and 29 is given as:

Since there's not any common factor

Hence, HCF(17, 23, 29) = 1

(3)

Prime factorization of 8 : 2 × 2 × 2 = 23

Prime factorization of 9 : 3 × 3 = 32

Prime factorization of 25 : 5 × 5 = 52

LCM of 8, 9, and 25 is given as:

LCM(8, 9, 25) = 23 × 32 × 52 = 8 × 9 × 25 =1800

HCF of 8, 9, and 25 is given as:

Since there's no common factor

Hence, HCF(8, 9, 25) = 1

Thus, (1) LCM(12, 15, 21) = 420, HCF(12, 15, 21) = 3 (2) LCM(17, 23, 29) = 11339, HCF(17, 23, 29) = 1 (3) LCM(8, 9, 25) = 1800, HCF(8, 9, 25) = 1

Answer 2

:

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-- :

Using prime factorisation method:

(i) 12, 15 and 21

Factor of 12=2×2×3

Factor of 15=3×5

Factor of 21=3×7

HCF (12,15,21)=3

LCM (12,15,21)=2×2×3×5×7=420

(ii) 17, 23 and 29

Factor of 17=1×17

Factor of 23=1×23

Factor of 29=1×29

HCF (17,23,29)=1

LCM (17,23,29)=1×17×23×29=11,339

(iii) 8, 9 and 25

Factor of 8=2×2×2×1

Factor of 9=3×3×1

Factor of 25=5×5×1

HCF (8,9,25)=1

LCM (8,9,25)=2×2×2×3×3×5×5=1,800