# Tips on finding LCM in radians?

1. Mar 2, 2017

### Giu1iano

1. The problem statement, all variables and given/known data
Lets say I want to find the LCM of -5π/3 and π/2; Also lets say these points are on the Unit Circle. ​

2. Relevant equations
It's easier to convert to degrees then back to radians but I don't want do that anymore because it's tedious

3. The attempt at a solution
Thoughts?

2. Mar 2, 2017

### BvU

Please explain: in my perception these numbers are not on the unit circle. And points don't have an LCM

3. Mar 2, 2017

### BvU

But if you mean the LCM of ${180\over \pi}\displaystyle \arg(e^{-i {5 \pi\over 3}})$ and ${180\over \pi} \arg(e^{i { \pi\over 2}})$ then there's light ! You can forget the common factors and look for the LCM of -5/3 and 1/2. I think that's 5 (-5?), so in your lingo $\pm 5\pi$ is the answer which I am in fact forbiddden to give because of the PF rules and guidelines. Or perhaps more explicitly ${180\over \pi} \arg(e^{i { \pm 5\pi}})$ (which still is a tedious conversion...)
But I count on your having found that already in the 'tedious' manner... ?

4. Mar 2, 2017

### BvU

After a beer, I see something else that escaped me: what is -300 degrees if you want to find an LCM ? Should I replace that with +60 (which in fact is equal to ${180\over \pi}\displaystyle \arg(e^{-i {5 \pi\over 3}})\ \$) and end up with 180 as LCM ?

5. Mar 2, 2017

### Giu1iano

I realized that say -(5π/3) is the same as -(10π/6) and (π/2) is the same as (3π/6), now I have a LCM or lowest common multiple. I can now do 3π - 5π/6 = -(2π/6).

6. Mar 2, 2017

### Giu1iano

I was plotting a sine graph at the time.

7. Mar 2, 2017

### haruspex

It would help if you were to explain exactly what you were doing and why it came down to finding the LCM of two angles. We would then have a better understanding of what LCM would mean in this context.
Are you trying to find how long before two waves of different wavelengths get back into phase?

8. Mar 2, 2017

### Staff: Mentor

No.

Your question really has nothing to do with radians or degrees or anything about angles -- it is a simple question about arithmetic; specifically how to add fractions.

How much is $3 - \frac 5 6$? According to your work above, it would be $-\frac 2 6$. Does that even make sense? If you subtract a number that is less than 1 from 3, would you get a negative number?

Last edited: Mar 2, 2017