Final answer:
The HCF of 126 and 234 is 18, obtained by multiplying the lowest powers of common prime factors (2 and 3²). The LCM is 2574, found by taking the highest powers of all primes involved (2, 3², 7, and 13).
Step-by-step explanation:
To find the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of 126 and 234, we will use prime factorization. Let's break down each number into its prime factors:
The HCF is the product of the lowest powers of common primes. Here, that's 2 × 3² = 18. For the LCM, we take the highest powers of all primes involved: 2 × 3² × 7 × 13 = 2574.
Therefore, the HCF of 126 and 234 is 18, and the LCM is 2574.