Questions: Find the least common multiple of 7c^2 and 5m.

Transcript text: Find the least common multiple of $7 c^{2}$ and $5 m$.

Solution

Solution Steps

To find the least common multiple (LCM) of two algebraic expressions, we need to consider both the numerical coefficients and the variable parts separately. The LCM of the numerical coefficients is the smallest number that is a multiple of both coefficients. For the variable parts, we take the highest power of each variable present in either expression.

Step 1: Identify the Expressions

We are given two expressions: \[ expr1 = 7c^2 \] \[ expr2 = 5m \]

Step 2: Find the LCM of the Coefficients

The numerical coefficients of the expressions are $7$ and $5$. The least common multiple (LCM) of $7$ and $5$ is calculated as: \[ \text{LCM}(7, 5) = 35 \]

Step 3: Combine the Variable Parts

Next, we consider the variable parts of the expressions. The variable $c$ appears in $expr1$ with the highest power of $2$, and the variable $m$ appears in $expr2$ with the power of $1$. Therefore, the LCM of the variable parts is: \[ c^2 \cdot m \]

Step 4: Formulate the Final LCM Expression

Combining the LCM of the coefficients and the variable parts, we have: \[ \text{LCM}(7c^2, 5m) = 35c^2m \]