Answer:
64×81×25×49×11×13×···×89×97.
Explanation:
The smallest positive integer divisible by the integers 1 through 99 will be the least common multiple (LCM) of the integers 1-99.
We then must find the largest power of all the primes up to 99 appearing in any of the integers up to 99.
For 2, the largest power is
.
For 3, the largest power is
.
For 5, the largest power is 5² = 25.
For 7, the largest power is 7² = 49.
For all primes p in 11-97, the largest power is p.
So, the LCM of all the numbers is then
.