You need the lowest common multiple of 48 and 54. Use whatever method

you have been shown to find this.

One way is to use the prime decompositions of the two numbers: 48=2^4*3, and 54=2*3^3, so lcm(48,54)= 2^4*3^3 = 432

So it is the 432nd egg that is checked for both qualities.

RonL