tom has guitar lessons every fifth day and piano lessons every third day. if she had a guitar lesson and a piano lesson on october 12 when will be the next date on which she has both guitar and piano lessons

In thirty days. The least common multiple of the two is 30 (5x6), and this would be the next day that you would have both.

Step-by-step explanation:

make a list

5th day so  

5,10,15,20,25,30,35,40

6th day is  

6,12,18,24,30

the corresponding day is 30 so the answer is 30