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 = 22 × 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) = 22 × 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= 24 × 3 × 7
54 = 2 × 33
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)= 24 × 33 × 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.