Three cars were racing along different tracks. The track distances for Car A, B and C were 3 km, 4 km and 7.5 together respectively. Given that they started at the same time, find the distance that the three cars covered so that they arrived at their respective starting points together.
To find the distance that the three cars covered so that they arrived at their respective starting points together, we need to find the least common multiple (LCM) of the three track distances.
The prime factorization of 3 km is 3.
The prime factorization of 4 km is 2^2.
The prime factorization of 7.5 km is 2 * 3 * 2.5.
To find the LCM, we need to take the highest power of each prime factor that appears in the factorizations:
- The highest power of 2 is 2^2 = 4.
- The highest power of 3 is 3.
- The highest power of 2.5 is 2.5.
Therefore, the LCM of the three track distances is 2^2 * 3 * 2.5 = 60 km.
Therefore, the three cars covered a distance of 60 km to arrive at their respective starting points together.