28. A teacher wrote down three positive integers on the whiteboard: $1125,2925, N$, and asked her class to compute the least common multiple of the three numbers. One student misread 1125 as 1725 and computed the least common multiple of 1725,2925 and $N$ instead. The answer he obtained was the same as the correct answer. Find the least possible value of $N$.
28. Answer: 2875
We look at the prime factorizations of 1125,2925 and 1725 . We have
$$
1125=3^{2} \times 5^{3}, 2925=3^{2} \times 5^{2} \times 13,1725=3 \times 5^{2} \times 23 \text {. }
$$

Since
$$
\operatorname{LCM}\left(3^{2} \times 5^{3}, 3^{2} \times 5^{2} \times 13, N\right)=\operatorname{LCM}\left(3 \times 5^{2} \times 23,3^{2} \times 5^{2} \times 13, N\right)
$$
we see that the least possible value of $N$ is $5^{3} \times 23=2875$.