No numbers exist. Not even the positive integers exist.

Is there a largest rational number?

it's undefined. There is no largest rational no.

How do you find the largest rational number?

Hint: We are given two rational numbers and we need to find out the greatest rational number between them. For that, we will Take LCM of all the rational numbers and after that compare its numerator. The rational number with a greater numerator will be the greatest rational number.