Find the least common multiple of 10c^3 and 4c^2 square

To find the least common multiple (LCM) of \(10c^3\) and \(4c^2\), we need to follow these steps:<br /><br />1. **Factorize the coefficients and the variables:**<br /> - \(10c^3 = 2 \cdot 5 \cdot c^3\)<br /> - \(4c^2 = 2^2 \cdot c^2\)<br /><br />2. **Identify the highest powers of all prime factors and variables:**<br /> - The prime factors are \(2\) and \(5\).<br /> - The highest power of \(2\) is \(2^2\).<br /> - The highest power of \(5\) is \(5^1\).<br /> - The highest power of \(c\) is \(c^3\).<br /><br />3. **Multiply these highest powers together to get the LCM:**<br /> \[<br /> \text{LCM} = 2^2 \cdot 5^1 \cdot c^3<br /> \]<br /><br />4. **Calculate the product:**<br /> \[<br /> 2^2 = 4<br /> \]<br /> \[<br /> 4 \cdot 5 = 20<br /> \]<br /> \[<br /> 20 \cdot c^3 = 20c^3<br /> \]<br /><br />Therefore, the least common multiple of \(10c^3\) and \(4c^2\) is \(\boxed{20c^3}\).