Sum of three consecutive even Integers is 54. Find the least among them.

Options

A. 18
B. 15
C. 14
D. 16

Answer

To solve the problem of finding the least among three consecutive even integers whose sum is 54, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
Let the smallest even integer be represented as \( x \). The next two consecutive even integers can then be expressed as \( x + 2 \) and \( x + 4 \).

2. **Set Up the Equation**:
According to the problem, the sum of these three integers is 54. Therefore, we can write the equation:
\[ x + (x + 2) + (x + 4) = 54 \]

3. **Combine Like Terms**:
Simplifying the left side of the equation gives:
\[ x + x + 2 + x + 4 = 54 \]
This simplifies to:
\[ 3x + 6 = 54 \]

4. **Isolate the Variable**:
To solve for \( x \), first subtract 6 from both sides:
\[ 3x = 54 - 6 \]
Which simplifies to:
\[ 3x = 48 \]

5. **Solve for \( x \)**:
Now, divide both sides by 3:
\[ x = \frac{48}{3} \]
This gives:
\[ x = 16 \]

6. **Identify the Three Integers**:
The three consecutive even integers are:
\[ 16, 18, 20 \]

7. **Conclusion**:
The least among these integers is:
\[ \text{Least Integer} = 16 \]

### Final Answer:
The least among the three consecutive even integers is **16**.

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