The boys were aged 4 and 10. The driver of the car, believed to be the boy's mother, and another female passenger, remain in a stable condition in hospital.
The crash occurred on the northbound carriageway near junction 15 at around 11.25am this morning.
The motorway has now reopened.
More top news
Unsettled and cold, with rain, sleet and snow
Granada Reports Political Correspondent Daniel Hewitt blogs on the challenge faced by Jeremy Corbyn at next week's local elections.
Here are all the candidates standing in the 2016 local election in Rossendale.