For this problem you want to find the LCM of 2 and 15. Since there are no common factors (besides 1), multiply them to find the LCM.
If it's hard for you to understand the word problem, think of everything as numbers first. "Every two days" means she waters them on day 2, day 4, day 6, and so on. "Every 15 days" means she trims them on day 15, day 30, day 45, etc. Now you know you're actually finding the multiples of 2 and 15. "She did both today" means the two tasks share a common day, which is day 30. "When will she do both again?" asks how far away the next common day will be, which is in another 30 days. So your LCM is 30.
I hope this helps you with future word problems!