Final answer:
To find the LCM and HCF of two numbers using prime factorization, find the prime factors of each number and then take the highest power of each prime factor for LCM and the lowest power for HCF.
Step-by-step explanation:
To find the LCM and HCF using the prime factorization method for the given pair of positive integers, 225 and 240, we need to first find the prime factors of both numbers.
Prime factorization of 225: 225 = 3 x 3 x 5 x 5 = 3^2 x 5^2
Prime factorization of 240: 240 = 2 x 2 x 2 x 2 x 3 x 5 = 2^4 x 3 x 5
To find the LCM, we need to take the highest power of each prime factor that appears in either number. LCM = 2^4 x 3 x 5^2 = 2 x 2 x 2 x 2 x 3 x 5 x 5 = 1200
To find the HCF, we need to take the lowest power of each common prime factor. HCF = 3 x 5 = 15