Question

Ursala and Omar are each building toy train tracks using different-sized pieces. Ursala has pieces that are 8 inches long, and Omar has pieces that are 18 inches long. Ursala and Omar build tracks that are the same length. How long are their tracks?

20 inches

144 inches

72 inches

36 inches

Answer 1

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**.