What is the least common multiple of 72 and \( 120 ? \) \( \begin{array}{ll}\text { A } 90 \\ \text { B } 260 \\ \text { C } 2160 \\ \text { D } 24\end{array} \)

To find the least common multiple (LCM) of 72 and 120, we can start by breaking down each number into its prime factors. For 72: \( 72 = 2^3 \times 3^2 \) For 120: \( 120 = 2^3 \times 3^1 \times 5^1 \) Next, to find the LCM, we take the highest power of each prime factor present in either number: - For 2, the highest power is \( 2^3 \) - For 3, the highest power is \( 3^2 \) - For 5, the highest power is \( 5^1 \) Now, we can calculate the LCM: \( \text{LCM} = 2^3 \times 3^2 \times 5^1 = 8 \times 9 \times 5 = 360 \) So, the least common multiple of 72 and 120 is \( 360 \). Now, let's compare this with the options given: \( \begin{array}{ll}\text { A } 90 \\ \text { B } 260 \\ \text { C } 2160 \\ \text { D } 24\end{array} \) None of these match our calculation; there's an error in this set of options as we concluded \( 360 \) is the correct answer!