Given, a+b+c=5 and a,b,c∈N L is least value of 2a3b5c and M is the greatest value of 2a3b5c. Possible pairs of (a,b,c)
≡(1,1,3),(1,3,1),(3,1,1),(1,2,2),(2,1,2),(2,2,1)
Value for (1,1,3)≡(2⋅3⋅53)=750 Value for (1,3,1)≡(2⋅33⋅5)=270 Value for (3,1,1)≡(23⋅3⋅5)=120 Value for (1,2,2)≡(21⋅32⋅52)=450 Value for (2,1,2)≡(22⋅31⋅52)=300 Value for (2,2,1)≡(22⋅32⋅51)=180 L=23:3⋅5=120,M=2⋅3⋅53=750 ∴M−L=2⋅3⋅53−23⋅3⋅5=2⋅3⋅5(25−4) =2⋅3⋅5⋅21=2⋅32⋅5⋅7