Find the least common multiple. Write your answer as a constant times a product of single variables raised to exponents. Submit

To find the least common multiple (LCM) of integers, you often break them down into their prime factors. For example, consider the numbers 12 and 18. The prime factorization of 12 is \(2^2 \times 3^1\) and for 18, it's \(2^1 \times 3^2\). To calculate the LCM, take each prime factor at its highest exponent: \(2^2\) from 12 and \(3^2\) from 18. Thus, the LCM is \(2^2 \times 3^2 = 36\). This approach can be applied to find the LCM of larger sets of numbers or even variables in algebra. Just remember to always use the highest power of each unique prime factor that appears in any of the factorizations. So if you have \(a^3\) and \(a^2\), for the LCM, you'll take \(a^3\). Hence, the expression would look like a constant times a product of variables raised to their respective maximum exponents, demonstrating a neat relationship in mathematics!