Question

Use the Prime Factorization Method. Along a highway there are electric poles on one side of the highway, and on the other cell phone towers and telegraph poles. The electric poles are separated by 38 feet, the telegraph poles are separated by 6 feet, and the cell phone towers by 144 feet. If all the poles are present at one point, of what point along the highway will all three be present again?

A) 3 feet
B) 12 feet
C) 18 feet
D) 36 feet

Answer 1

To find the point along the highway where all three types of poles will be present again, we need to find the least common multiple (LCM) of the distances between the poles. Using the prime factorization method, the LCM is 576 feet.

Step-by-step explanation:

We need to find the point along the highway where all three types of poles (electric poles, telegraph poles, and cell phone towers) will be present again.

To do this, we need to find the least common multiple (LCM) of the distances between the poles. The distances are 38, 6, and 144 feet.

We can find the LCM using the prime factorization method.

First, we factorize each distance: 38 = 2 × 19, 6 = 2 × 3, and 144 = 2^4 × 3^2.

Next, we take the highest power of each prime factor: 2^4 × 3^2 × 19 = 576.

Therefore, all three types of poles will be present again every 576 feet along the highway.