##### NCERT Solutions for Class 10 Maths | Chapter: Real Numbers | Concept: Compute LCM & HCF by Prime Factorization. Properties of product of LCM and HCF of 2 numbers

#### Question 2: Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = product of the two numbers.

i. 26 and 91

ii. 510 and 92

iii. 336 and 54

#### Explanatory Answer

##### i. 26 and 91

Step 1: Prime factorize the numbers

26 = 2 × 13

91 = 7 × 13

Step 2: **Compute HCF**: HCF = Product of the lowest powers of common primes in the 2 numbers.

HCF (26, 91) = 13

Step 3: **Compute LCM**: LCM = Product of the highest powers of all the primes in the 2 numbers.

LCM (26, 91) = 2 × 7 × 13 = 182

Step 4: Verifying product of LCM and HCF of 2 numbers = Product of the 2 numbers

LCM × HCF = 13 × 182 = 2366

Product of 26 and 91 = 26 × 91 = 2366

##### ii. 510 and 92

Step 1: Prime factorize the numbers

510 = 2 × 3 × 5 × 17

92 = 2^{2} × 23

Step 2: **Compute HCF**: HCF = Product of the lowest powers of common primes in the 2 numbers.

HCF (510, 92) = 2

Step 3: **Compute LCM**: LCM = Product of the highest powers of all the primes in the 2 numbers.

LCM (510, 92) = 2^{2} × 3 × 5 × 17 × 23

= 23460

Step 4: Verifying product of LCM and HCF of 2 numbers = Product of the 2 numbers

LCM × HCF = 2 × 23460 = 46920

Product of 510 × 92 = 46920

##### iii. 336 and 54

Step 1: Prime factorize the numbers

336= 2^{4} × 3 × 7

54 = 2 × 3^{3}

Step 2: **Compute HCF**: HCF = Product of the lowest powers of common primes in the 2 numbers.

HCF (336, 54) = 2 × 3 = 6

Step 3: **Compute LCM**: LCM = Product of the highest powers of all the primes in the 2 numbers.

LCM (336, 54)= 2^{4} × 3^{3} × 7 = 3024

Step 4: Verifying product of LCM and HCF of 2 numbers = Product of the 2 numbers

LCM × HCF = 6 × 3024 = 18144

Product of 336 and 54 = 336 × 54 = 18144.