Security lights have been erected along both sides of a street in Nakuru town.The lights are 50 metres apart along the right-hand side of the road and 80 metres apart on the left-hand side.At one end of the road,two lights are directly opposite each other.Find the total number of lights that will be erected when the poles are directly opposite each other again at the end of the road

Question

Security lights have been erected along both sides of a street in Nakuru town.The lights are 50 metres apart along the right-hand side of the road and 80 metres apart on the left-hand side.At one end of the road,two lights are directly opposite each other.Find the total number of lights that will be erected when the poles are directly opposite each other again at the end of the road

Answer 1

To find the total number of lights that will be erected when the poles are directly opposite each other again at the end of the road, we need to find the least common multiple (LCM) of 50 and 80.

The prime factorization of 50 is 2 * 5^2.
The prime factorization of 80 is 2^4 * 5.

To find the LCM, we take the highest power of each prime factor that appears in either number:
LCM = 2^4 * 5^2 = 16 * 25 = 400.

Therefore, there will be a total of 400 lights erected when the poles are directly opposite each other again at the end of the road.