Step 1 :Let the number of containers be \(n = 24\) and the capacity of each container be \(c = 14.9\) litres.
Step 2 :Calculate the total capacity of all containers: \(n \times c = 24 \times 14.9 = 357.6\) litres.
Step 3 :Since Katya can only buy a whole number of litres, round down the total capacity to the nearest whole number: \(\lfloor 357.6 \rfloor = 357\) litres.
Step 4 :\(\boxed{357}\) litres is the maximum amount of oil Katya can buy to fit into her containers.