Okay, this is a classic head-scratcher, but here are some possibilities and troubleshooting steps, keeping in mind the coin-operated aspect which introduces more complexity

Possible Causes:

1. Neutral-Ground Faults

This is the MOST LIKELY culprit, especially in older buildings.

In the Laundry Circuit

A small current is leaking from the neutral to ground somewhere in the washing machine circuit. When the dryer kicks on, it adds just enough additional load to the neutral to cause the GFCI to trip.

Shared Neutral

While each appliance should be on its own circuit, it's possible an overloaded shared neutral exists somewhere, especially if the building was wired a long time ago. The dryer's load is then pushing current back onto the neutral feeding the washer circuit.

Dryer to Water Line

With gas dryers, there might be a poor ground and a partial ground fault path through the gas line/water pipes connected to the building ground.

Commercial Washer Problem

Coin-operated washers are more complex and might have a problem in the circuitry powering the coin mechanism itself, which creates a small neutral-ground fault that gets exacerbated when the dryer runs.2.

GFCI Sensitivity/Compatibility



Old GFCI/Sensitive GFCI

The GFCI might just be overly sensitive, and the small amount of normal leakage in the system is enough to trip it, especially with the added load of the dryer. This is less likely if multiple GFCIs are doing this.

Harmonics

LED lights and even modern appliances can generate harmonics that might interfere with the GFCI's operation. This is a less common but possible issue, especially since you installed LEDs around the same time.3.

Voltage Drop/Weak Neutral



Panel Issues

A loose neutral connection in the panel itself could be causing voltage fluctuations when the dryer loads up the system. This could then cause the GFCI to falsely interpret a ground fault.

High Resistance Connections

Corroded or loose connections in the wiring anywhere between the panel and the outlets (including the dryer outlets) could be causing voltage drop, leading to erratic behavior.4.

Wiring Errors



Accidental Neutral/Ground Bonds

In subpanels or at the outlet boxes, a neutral wire and a ground wire might be accidentally touching.

Miswired Dryer Receptacle

While you didn't touch the dryer circuits, someone else might have wired the dryer receptacle incorrectly in the past (e.g., neutral and ground reversed). This would send current through the ground when the dryer is running, causing the GFCI to trip.

Troubleshooting Steps (Systematic Approach is Key)


Visual Inspection (First and Foremost)



Panel

Carefully examine the panel. Look for loose connections, signs of corrosion, burned wires, or anything unusual, especially around the neutral bar and ground bar.

SAFETY FIRST! TURN OFF THE MAIN BREAKER IF YOU ARE NOT COMFORTABLE WORKING IN A PANEL! Wiring at Outlets

Check the wiring at the washer outlet, the dryer outlets, and any accessible junction boxes in the circuit. Look for loose connections, damaged insulation, or signs of overheating.

Check the Grounding Wire

Ensure the ground wire is connected properly at the washer and dryer outlets and runs back to the panel.2.

Testing with a Multimeter



Voltage Drop Test

With the dryer running, measure the voltage at the washer GFCI. Then, measure the voltage at the panel. A significant voltage drop between the panel and the outlet when the dryer is on could indicate a problem. Test all legs.

Neutral-Ground Voltage Test

With the dryer OFF, measure the voltage between the neutral and ground wires at the washer GFCI receptacle. It should be close to zero (ideally under 1V). With the dryer ON, measure it again. A significant increase in neutral-ground voltage when the dryer is running points to a neutral-ground fault somewhere.

Continuity Test



WITH THE CIRCUIT DE-ENERGIZED AND DISCONNECTED! Use a multimeter to check continuity between the neutral and ground wires at the washer receptacle. You should NOT have continuity (infinite resistance). If you do, you have a neutral-ground fault. Important: Disconnect the neutral wire from the neutral bar in the panel before performing this test to avoid false readings from other circuits.3. Isolate the Issue



Turn OFF the Dryers

Turn off the breakers for both dryers. Does the GFCI still trip randomly? If so, the issue is likely in the washer circuit itself.

One Dryer at a Time

Turn on only one dryer at a time and see if you can isolate which dryer is causing the problem.

Disconnect the Coin Mechanism (If Possible)

If you can safely disconnect the coin mechanism on one of the washers, try that and see if it resolves the issue. This can help rule out a fault in the coin mechanism itself.4.

GFCI Replacement (Consideration)

If you've ruled out everything else, try replacing the GFCI with a new one. Sometimes, GFCIs can become faulty or overly sensitive. Make sure you use a good quality GFCI.5.

LED Lighting Since the problem started around the same time, turn OFF the lighting and repeat the test. LED's are known to cause issues.

Important Considerations



Older Wiring

Be extremely careful when working with older wiring. The insulation can be brittle and prone to cracking.

Coin-Operated Equipment

Coin-operated equipment can have complex wiring and grounding configurations. Consult the manufacturer's documentation if possible.

Licensed Electrician

If you are not comfortable working with electrical wiring, especially in an older building, call a licensed electrician. This is especially important if you suspect a neutral-ground fault or a panel issue.

Here's a logical process to start with


Begin with the Visual Inspection of the Panel

Focus on the neutral and ground bars.2.

Perform the Neutral-Ground Voltage Test

Both with dryers on and off.3.

Isolate which dryer is the culprit.4. If a specific dryer is tripping the GFCI, carefully inspect the dryer outlet and wiring.5. If the problem persists, and you're comfortable, perform the continuity test between neutral and ground at the washer receptacle with the circuit de-energized and the neutral disconnected from the panel.

Good luck! This is a challenging problem, but with careful troubleshooting, you should be able to find the cause. Let me know what you find, and we can refine the troubleshooting steps! Flag for review