The numbers $1, 2, \ldots, 100$ are written on a board. At each step, all numbers that do not have any divisors among the non-erased numbers, except for themselves, are erased simultaneously. For example, on the first step, only the number 1 is erased. Which numbers will be erased on the last step?
On the next step, after erasing the unit, all prime numbers (which have no divisors other than 1 and themselves) will be erased. Next, the numbers that have exactly two prime factors (not necessarily distinct) in their factorization will be erased, followed by the numbers that have exactly three prime factors, and so on. Since $2^{7}>100$, there are no numbers among the given ones that have more than six prime factors in their factorization. Therefore, on the last step, the numbers that have exactly six prime factors will be erased. Since

$3^{2} \cdot 2^{4}>100$, there are only two such numbers: $2^{6}=64$ and $3 \cdot 2^{5}=96$.

## Answer

64 and 96.