We know that the reactant ratios
a : b : c
are
3 : 1 : 2
So we will check the amount of the other two reactants required by taking one as the base.
With a as the base,
2.3 : 0.77 : 1.53
The amounts of b and c required for 2.3 moles of a are present
With b as the base,
4.8 : 1.6 : 3.2
Both a and c are present in amounts less than that required for 1.6 moles of b.
With c as the base,
4.65 : 1.55 : 3.1
Only a is limiting in this case
From the above considerations, we see that a is always in quantities less than that which would be required, so a is the limiting reactant.
