Mr. Hon purchases a new car every 4 years. Ms. Jasper purchases a new car every 6 years. They both purchased new cars this year. When will they next both purchase new cars in the same year?
To find out when Mr. Hon and Ms. Jasper will next purchase new cars in the same year, we need to find the least common multiple (LCM) of 4 and 6, since the LCM represents the smallest shared multiple of both numbers.
The prime factors of 4 are 2 and 2 (2 x 2).
The prime factors of 6 are 2 and 3 (2 x 3).
To find the LCM, we take the highest power of each prime factor that appears in either number:
2 x 3 x 2 = 12
Therefore, Mr. Hon and Ms. Jasper will next purchase new cars in the same year in 12 years.