I haven't seen my approach in the comments yet and figured it may help out anyone else trying to wrap their head around it.

Alternative to the GCD approach (well documented below), I mentally wanted to find the largest square that was divisible by both l and b. It's not the most efficient, but it's how I saw the solution:

Python3

def restaurant(l, b):
    squares = [x**2 for x in range(1, 1001)]
    mult = l*b
    final_squares = mult

    l_divisors = [i for i in range(1, l + 1) if l % i == 0]
    b_divisors = [i for i in range(1, b + 1) if b % i == 0]

    if l == b:
        final_squares = 1
    else:
        mult_divisors = [i for i in range(1, mult + 1) if mult % i == 0]

        for mult_div in mult_divisors:
            if mult_div in squares:
                if (mult_div**(1/2) in l_divisors) and (mult_div**(1/2) in b_divisors):
                    final_squares = mult / mult_div

    return int(final_squares)