The third victim was a 50-year-old man.
The teenagers had found the bomb in a nearby jungle and brought it back home to their Bhandara village, said Government administrator Maheswor Newpane.
He added that the bomb probably exploded when the teenagers, who were unaware that it was an explosive, were playing with it.
In a similar incident in India's Manipur, three children were killed when an explosive they found on the road detonated when they were playing with it.
The explosive was believed to be left behind by Maoists targeting security forces.