Problem
Find the Lowest Common Multiple (LCM) of the expressions \(2x^2y\), \(8xy^2\), and \(16x^2y^3\).
Solution
Step 1 ：Step 1: First, we factorize each of the expressions into their prime factors. \(2x^2y = 2 \cdot x \cdot x \cdot y\), \(8xy^2 = 2 \cdot 2 \cdot 2 \cdot x \cdot y \cdot y\) and \(16x^2y^3 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot x \cdot x \cdot y \cdot y \cdot y\).
Step 2 ：Step 2: Next, we identify the highest power of each prime factor in the three expressions. For 2, it is \(2^4\). For \(x\), it is \(x^2\). For \(y\), it is \(y^3\).
Step 3 ：Step 3: The LCM is then the product of each of these highest powers, i.e., \(2^4 \cdot x^2 \cdot y^3\).
