The important part for LEDS and the sockets of the rainbow cables is that the legs of the LEDs have a thickness of 0.45mm or greater.   Some LEDs have legs that are approximately 0.37mm, and they are too loose when connected to the cables. However, here's a great set available on Amazon for just 3 cents per LED, and that we've verified have the correct thickness of the LED legs.

DiCUNO 450pcs(5 colors x 90pcs) 5mm LED Light Emitting Diode Round Assorted Color White/Red/Yellow/Green/Blue Kit Box

Available on Amazon for approximately $15.00

($0.03 per LED)