Explanation

N ≡ 2 (mod 6), 8 (mod 12), 11 (mod 15), 20 (mod 24). Adding 4: N+4 is divisible by 6, 12, 15 and 24, so N+4 is a multiple of lcm(6,12,15,24) = 120. Thus N = 120t − 4; the largest 5-digit value uses t = 833, giving N = 99960 − 4 = 99956. This is option B.