# Question #56258

##### 1 Answer

Feb 20, 2018

15

#### Explanation:

The sine function has a period of

Thus

Similarly, it is easy to see that the periods of the second and third terms in the sum are 3 and 5, respectively.

So, the there terms repeat whenever

The sum will repeat when each of them repeats together - for this,

The period of the sum is, then, the **least** common multiple of 1, 3 and 5 - that is, 15.