BdMO Online Forum

Problem 10:
The $n$-th term of a sequence is the least common multiple (l.c.m.) of the integers from $1$ to $n$. Which term of the sequence is the first one that is divisible by $100$?

\[100=2^2.5^2\]
We first get $25$ at $25^{th}$ term.That term is also divisible by $2^2$.So the answer is $25^{th}$ term.

Can you explain this logically?

He means to divide $100$ the term must divide $2^2,5^5$ the first term that divides $25$ is the $25^{th}$ term and it also divides $4$.That's why