Question

Find by prime factorisation the LCM of the numbers 18180 and 7575. Also, find the HCF of the two numbers.

Answer 1

Given: 18180 and 7575.

Step-wise calculation:

1. Prime factorisation:

18180 = 1818 × 10

= (909 × 2) × (2 × 5)

= 2² × 3² × 5 × 101

7575 = 25 × 303

= 5² × (3 × 101)

= 3 × 5² × 101

2. HCF = Product of common primes with smallest powers:

Common primes: 3¹, 5¹, 101¹

HCF = 3 × 5 × 101

= 15 × 101

= 1515

3. LCM = Product of all primes with highest powers:

Take 2², 3², 5², 101¹

LCM = 2² × 3² × 5² × 101

= 4 × 9 × 25 × 101

= 900 × 101

= 90900