Does any LED lamp work with any soak off gel system? Shellac, Gelish etc

Yes normally to take the gels off any LED lamp will work but to do the set the gels you will need the LED lamp recommended.

Hi Vickie
The Gelish system uses either a special LED lamp or a 36 watt UV Lamp. Nail Harmony UK supply both versions which have different price points. I don't believe a LED lamp will cure any other gel products as the LED lamp sold by Nail Harmony is specific for the Gelish system.
UV lamps are more versatile and MAY work with more than one system. It is best to speak to the experts (CND/SweetSquared, Nail Harmony etc) and get the full specifications of their lamps. Some people claim their UV lamp works with all systems and the product appears to cure correctly but clients may come across issues later on.
Hope this helps.
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To ensure that your product performs correctly you must use the lamp recommended by the manufacturer.
It is a common misconception that any 36 watt uv lamp will cure Gel polishes, if you use the incorrect lamp you may cause under or over curing leading to product breakdown.