Question

J and P both take dance lessons. J has a lesson every 4 days and P has one every 3 days. If they both had a lesson today, how many days will it be until they have a lesson on the same day again? a) 6 days b) 7 days c) 8 days d) 12 days

Answer 1

To find out how many days it will be until J and P have a lesson on the same day again, you need to find the least common multiple (LCM) of their lesson schedules, which are every 4 days for J and every 3 days for P.

The LCM of 4 and 3 is the smallest number that both 4 and 3 can evenly divide into. You can find the LCM using the following steps:

1. List the multiples of 4: 4, 8, 12, 16, 20, 24, ...

2. List the multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...

The smallest number that appears in both lists is 12. So, the LCM of 4 and 3 is 12.

Therefore, J and P will have a lesson on the same day again every 12 days.

So, the correct answer is (d) 12 days.

Explanation: