To find the lengths of the toy train tracks that Ursala and Omar can build, we need to determine the least common multiple (LCM) of the lengths of their pieces: 8 inches (Ursala) and 18 inches (Omar).
First, let's find the prime factorization of each length:
- 8 can be factored into \(2^3\).
- 18 can be factored into \(2^1 \times 3^2\).
Next, to find the LCM, we take the highest power of each prime number that appears in these factorizations:
- For the prime number 2, the highest power is \(2^3\) (from 8).
- For the prime number 3, the highest power is \(3^2\) (from 18).
Now, we calculate the LCM:
\[ \text{LCM} = 2^3 \times 3^2 = 8 \times 9 = 72 \]
Thus, both Ursala and Omar can build tracks that are 72 inches long. Therefore, the answer is:
72 inches.
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