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., \(2^4 \cdot x^2 \cdot y^3\).

From Solvely APP
Source: https://solvelyapp.com/problems/KeCVQhWp6f/

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