Question

Let A = lcm [1, 2, 3, ..., 99] and B = lcm [1, 2, 3,..., 99, 100]. Compute B/A.

Answer 1

The LCM of {1, 2, 3, ..., 99} and {1, 2, 3, ..., 100} are the same, since 100 = 2² 5² doesn't contain any unique powers of primes - 2² = 4 and 5² = 25 are already accounted for. So

`\frac BA = \boxed{1}`