Question

. 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.

Answer 1

Note that

• 12=2·2·3;
• 20=2·2·5;
• 36=2·2·3·3.

The common factors of these three numbers are 2, 2. Also numbers 12 and 36 have one more common factor 3, then the least common multiple is

LCM(12,20,36)=2·2·3·5·3=180 sec=3 min (here first you write all common factors between all three numbers, then between two numbers and at last all remaining factors).

Answer: all three experiments will need to be checked after 3 minutes passed, then after 6 minutes passed, then after 9 minutes passed and so on.