Question: Find the least common multiple of $5x^3$ and $7n^4$.

Solution

To find the least common multiple (LCM) of \(5x^3\) and \(7n^4\), we follow these steps: Identify the different bases and their respective powers in the expressions. The terms are: \(5x^3\) and \(7n^4\). The bases are: 5, \(x\), 7, and \(n\). For the LCM, use the highest power of each base from the given terms. For 5, the highest power is \(5^1\). For 7, the highest power is \(7^1\). For \(x\), the highest power is \(x^3\). For \(n\), the highest power is \(n^4\). Combine these to find the LCM: \[ \text{LCM} = 5^1 \cdot 7^1 \cdot x^3 \cdot n^4 \] Simplify the expression: \[ \text{LCM} = 35x^3n^4 \] Thus, the least common multiple of \(5x^3\) and \(7n^4\) is \(35x^3n^4\).