Final answer:
The LCM of 18180 and 7575 is 546300, and the HCF is 1515, found by breaking down each number into its prime factors and selecting the highest and lowest powers of all primes appearing in both numbers respectively.
Step-by-step explanation:
To find the LCM (Least Common Multiple) and HCF (Highest Common Factor) of 18180 and 7575 using prime factorisation, we break down each number into its prime factors:
- 18180 = 2 x 2 x 3 x 5 x 303
- 7575 = 5 x 1515
We then further factorize 303 and 1515 as they are not prime:
- 303 = 3 x 101
- 1515 = 3 x 5 x 101
So the prime factorisation of 18180 becomes 2 x 2 x 3 x 3 x 5 x 101, and for 7575, it is 3 x 5 x 5 x 101.
To get the LCM, we multiply each prime factor the greatest number of times it appears in any of the numbers:
LCM = 2 x 2 x 3 x 3 x 5 x 5 x 101 = 546300
To find the HCF, we multiply together the lowest powers of all the primes that appear in both numbers:
HCF = 3 x 5 x 101 = 1515