At what times of the day between 10: 00 a. m. and 5: 00 p. m. do the chemistry presentation and the recycling presentation start at the same time?
science museum
-show schedule-
chemistry-every 10 minutes
electricity-every 20 minutes
recycling-every 6 minutes
fossils-every 45 minutes
the first showing for all shows is at 10: 00 a. m.

Okay, Chemistry runs every 10 minutes and the Recycling runs every 6 minutes. In order to find what time they both start at the same time you must find the lowest common multiple (if you are using mathematical terminology). To do this the long but visual way you can write out each of the times and find the first ones that are the same.
Chemistry: 10:00  10:10  10:20  10:30
Recycling:  10:00  10:06  10:12  10:18  10:24  10:30
As you can see both Chemistry and Recycling both have a LCM of 10:30 which tells us that the time for which both Chemistry and Recycling start at the same time during the show is 10:30AM.