The Business Secretary said the figure, if accepted by the Government, would be the first real-terms increase since 2008.
After disclosing the recommendation to a parliamentary committee, Mr Cable said: "It is faster than inflation and that is the first time in six years that has happened."
The LPC has suggested that the level for apprentices should rise by 2%.
The recommendation is below the increase from £6.31 to £7 that had been floated by allies of Chancellor George Osborne.
Mr Cable said the LPC had balanced "fairness against the risks to employment" if the level was set too high.
Mr Osborne said that the economic recovery meant "Britain can afford an above-inflation increase in the minimum wage so we can restore its real value".
Treasury analysis has suggested that increasing the National Minimum Wage to £7 by 2015-16 would only have a minor impact on unemployment.
TUC General Secretary Frances O'Grady said: "This is a welcome increase in the minimum wage, which starts to recover some of the ground it has lost since 2008.