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?
A.
in 2 years
B.
in 8 years
C.
in 12 years
D.
in 24 years
The least common multiple of 4 and 6 is 12. This means that both Mr. Hon and Ms. Jasper will next purchase new cars in the same year in 12 years. Therefore, the answer is C. in 12 years.
To find out when Mr. Hon and Ms. Jasper will both purchase new cars in the same year, we need to find the least common multiple (LCM) of their purchase intervals.
The purchase interval for Mr. Hon is 4 years, and the purchase interval for Ms. Jasper is 6 years.
The LCM of 4 and 6 is 12.
Therefore, both Mr. Hon and Ms. Jasper will next purchase new cars in the same year in 12 years.
The correct answer is C. in 12 years.
To determine 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. The LCM is the smallest number that is divisible by both 4 and 6.
To find the LCM, we can list the multiples of both 4 and 6 and find the smallest common multiple.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...
We can see that 12 is the smallest number that appears in both lists. Therefore, Mr. Hon and Ms. Jasper will next purchase new cars in the same year in 12 years.
Therefore, the correct answer is:
C. in 12 years