Dr. Abramson and her assistants are working on three different

experiments using water. Each experiment lasts for 15 minutes.

For the fi rst experiment, the water level must be checked

every 12 seconds. For the second experiment, the temperature

of the water must be checked every 30 seconds. For the third

experiment, the color of the water must be checked every 36

seconds. In minutes, list the times all three experiments will

need to be checked at the same time.

The correct answer is:

Every 6 minutes.

Explanation:

To find the intervals in which each of the 3 experiments must be checked at the same time, we must find the least common multiple of all 3 numbers. To do this, we find the prime factorization of each:

12 = 6 (2)

6 = 2 (3)

12 = 2 (2) (3)

30 = 10 (3)

10 = 2 (5)

30 = 2 (3) (5)

36 = 6 (6)

6 = 2 (3)

6 = 2 (3)

36 = 2 (2) (3) (3)

We first find the common factors. Between all 3 numbers, the only common factors are 2 and 3.

Next we multiply these common factors by the uncommon ones. The uncommon factors are 2, 2, 5 and 3:

2 (3) (2) (2) (5) (3) = 6 (2) (2) (5) (3) = 12 (2) (5) (3) = 24 (5) (3) = 120 (3) = 360

This means the least common multiple is 360. 360/60 = 6; this means every 3 minutes all 3 experiments will need to be checked.