Find the least common multiple (LCM) of 16xy^3 and 20x^3y^2

## Step 1: <br />First, we need to find the prime factorization of each term. <br /><br />## Step 2: <br />The prime factorization of 16 is \(2^{4}\), of \(x\) is \(x\), and of \(y^{3}\) is \(y^{3}\). So, the prime factorization of \(16xy^{3}\) is \(2^{4}xy^{3}\).<br /><br />## Step 3: <br />The prime factorization of 20 is \(2^{2} \times 5\), of \(x^{3}\) is \(x^{3}\), and of \(y^{2}\) is \(y^{2}\). So, the prime factorization of \(20x^{3}y^{2}\) is \(2^{2} \times 5x^{3}y^{2}\).<br /><br />## Step 4: <br />To find the least common multiple (LCM), we take the highest power of each prime factor that appears in either factorization. <br /><br />### The formula for LCM is: <br />### \(LCM = 2^{max(4,2)} \times 5^{max(0,1)} \times x^{max(1,3)} \times y^{max(3,2)}\)<br /><br />## Step 5: <br />Substitute the values into the formula to get the LCM.