what is the smallest non zero whole number that is divisible by both 176 and 342

To find the smallest non-zero whole number divisible by both 176 and 342, we need to calculate the **least common multiple (LCM)** of these two numbers.

The LCM can be found using the formula:

\[
\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}
\]

Where GCD is the greatest common divisor.

### Step 1: Find the GCD of 176 and 342
- Find the prime factorizations of 176 and 342:
  - \( 176 = 2^4 \times 11 \)
  - \( 342 = 2 \times 3^2 \times 19 \)

The only common factor is \( 2^1 \).

So, the **GCD(176, 342) = 2**.

### Step 2: Calculate the LCM
Now we apply the LCM formula:

\[
\text{LCM}(176, 342) = \frac{176 \times 342}{2}
\]

\[
176 \times 342 = 60192
\]
\[
\frac{60192}{2} = 30096
\]

Thus, the smallest non-zero whole number divisible by both 176 and 342 is **30,096**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the difference between LCM and GCD?
2. How can the Euclidean algorithm be used to find the GCD?
3. Can you explain prime factorization in more detail?
4. How is the LCM useful in solving real-world problems?
5. What is the process to find the LCM of more than two numbers?

**Tip**: Always double-check calculations, especially with prime factorizations, to avoid small mistakes in larger computations!

Discover how to find the smallest non-zero whole number divisible by both 176 and 342. This problem involves calculating the Least Common Multiple (LCM) using the Greatest Common Divisor (GCD) and prime factorization. Ideal for students in Grades 9-12.

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