Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is:

The transition equation for Lyman series is given by
1λ=R(11²−1n²)
for largest wavelength, n=2.
∴1λmax=R(11²−12²)
The transition equation for Balmer series is given by
1λ=R(12²−1n²)
for largest wavelength, n=3
∴1λmax=R(12²−13²)
Therefore,
λLmaxλBmax=(12²−13²)(11²−12²)=53634=527