Explanation: The Highest Common Factor (HCF) and the Least Common Multiple (LCM) are two important concepts in number theory. The HCF of two numbers is the largest number that divides both of them without leaving a remainder, while the LCM is the smallest number that is a multiple of both.
Given that the HCF of 72 and 120 is 24, we can use the relationship between HCF and LCM to find the LCM. The relationship is given by the formula:
\[ \text{HCF} \times \text{LCM} = \text{Product of the numbers} \]
Let's denote the LCM of 72 and 120 as \( \text{LCM}(72, 120) \). According to the formula:
\[ 24 \times \text{LCM}(72, 120) = 72 \times 120 \]
To find the LCM, we solve for \( \text{LCM}(72, 120) \):
\[ \text{LCM}(72, 120) = \frac{72 \times 120}{24} \]
First, we calculate the product of 72 and 120:
\[ 72 \times 120 = 8640 \]
Next, we divide this product by the HCF, which is 24:
\[ \text{LCM}(72, 120) = \frac{8640}{24} = 360 \]
Thus, the LCM of 72 and 120 is 360.
To verify, we can also use the prime factorization method. The prime factorization of 72 is \( 2^3 \times 3^2 \) and the prime factorization of 120 is \( 2^3 \times 3 \times 5 \). The LCM is found by taking the highest power of each prime factor present in the factorizations:
\[ \text{LCM}(72, 120) = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360 \]
Therefore, the correct answer is 360, which corresponds to option B.