https://r2.erweima.ai/mathbot/image/1725931423053zn3qac31.jpg

The expression shown in the image is:

\[
\text{Calcula} \, (2a - 1) ; \, \text{MCM}(6a, 3a) = 54
\]

This translates to: Calculate \( 2a - 1 \) given that the least common multiple (LCM, in Spanish "MCM") of \( 6a \) and \( 3a \) is 54.

### Step 1: Calculate the Least Common Multiple (LCM)
The LCM of \( 6a \) and \( 3a \) is given as 54. We can find \( a \) by solving this equation. 

The LCM of \( 6a \) and \( 3a \) is \( 6a \) since \( 6a \) is a multiple of \( 3a \). Therefore, we solve:

\[
6a = 54
\]

This gives:

\[
a = \frac{54}{6} = 9
\]

### Step 2: Substitute \( a = 9 \) into \( 2a - 1 \)

Now that we know \( a = 9 \), substitute into \( 2a - 1 \):

\[
2a - 1 = 2(9) - 1 = 18 - 1 = 17
\]

### Final Answer:

Thus, the value of \( 2a - 1 \) is 17.

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Do you have any questions or would you like further details?

Here are 5 related questions for further exploration:
1. How is the least common multiple (LCM) calculated for two algebraic expressions?
2. What is the difference between LCM and greatest common divisor (GCD)?
3. How would the equation change if we were asked for the GCD instead of the LCM?
4. Can the value of \( a \) be negative in this context?
5. How does the method change if the numbers inside the LCM were prime factors?

**Tip:** When solving for LCM or GCD in algebraic terms, first solve for the variables, then proceed with known number operations.

Learn how to solve for a in the equation where the LCM(6a, 3a) equals 54, and calculate 2a - 1. This algebra problem covers key concepts such as least common multiple (LCM) and solving linear equations. Suitable for students in Grades 6-8.

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