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
To find out when they will next both purchase new cars in the same year, we need to find the least common multiple (LCM) of 4 and 6.
The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, ...
The multiples of 6 are: 6, 12, 18, 24, 30, 36, ...
From the list, we can see that the least common multiple of 4 and 6 is 12.
Therefore, they will next both purchase new cars in the same year after 12 years.
The correct answer is: C. in 12 years.