I have one 15 amp GFI breaker in my main panel. We have two patio outlets, the garbage disposal and one outlet in each of the two bathrooms all wired common. Whenever we have company and women are using hair dryers at the same in each bathroom the breaker trips. Would it be OK to replace the 15 amp breaker with a 20 amp so it doesn't trip anymore when they are drying their hair?
A circuit is defined by its overcurrent protection (breaker) not the other way around. The circuit you are talking about was originally designed to be a 15A circuit not a 20A. What you really need to do is add two more 20A circuits, one for each bathroom. Here's why.
Your circuit trips while women are using hairdryers in 2 bathrooms. A standard hairdryer is rated 1500W on high. 1500W*2=3000W, 3000W/120V=25A, that is 5A higher than a 20A circuit breaker. So even if you were able to install a 20A breaker, there is a good chance you are still going to trip the breaker on that circuit.
You could do a few other things which might or might not be satisfactory, but in the end a substandard repair will render a substandard performance.
In conclusion do not change out a 15A breaker to a 20A without verifying that it is capable of being a 20A circuit. If for nothing else, it is against the law and might cause a shock or burn hazard. Sooner or later you are probably going to have to install two 20A circuits to each bathroom, so you might as well do it now. Then you will be done with it and it will be legal and most important the women will be happy.
Hope this helps and stay safe.
You can never "just up-size a breaker to stop it from tripping". 15A and 20A breakers cost the same. If it was safe to use a larger breaker, the builder would have already done it.
It wouldn't matter anyway
A hair dryer, like most heat appliances, is 1500W because that is the UL limit for such devices. Two hair dryers are 3000W.
The 15A circuit you have is rated for 1440W continuous or 1800W peak. The 20A circuit you want is rated for 1920W continuous or 2400W peak.
All of these numbers are well below 3000W. No receptacle circuit can support two heat appliances. That is a fact of life.
Upgrade the circuit
The only way to support dual hair dryers is with two circuits. With clever wiring in the right place, you can split the circuits into 2 or even 3 circuits.
Code currently requires that bathroom receptacle circuits serve no load outside a bathroom. It gives you two choices: one circuit can power receptacles only in any number of bathrooms (but you can see right now where that's a bad idea)... Or one circuit can power receptacles and other things only in one bathroom. That last one is the way to go. They need to be 20A circuits.
No, don't up-size the breaker. The breaker's job is to protect the wiring hidden inside the walls. The installer chose a 15 amp breaker because that was the code-approved rating to protect the specific wire used in that circuit. A higher-amperage breaker would put the wiring at risk of overheating and could lead to a fire.
There may be some other circuit near one of the bathrooms which could be extended to provide a new outlet in the bathroom. That would allow the hair tools to operate on different circuits. It would be necessary to add GFCI protection if this was to be done.