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====== Contest Info ======
date: 2020.7.11 23:05-01:05 (+1D)
[[https://codeforces.com/contest/1372/problem/B|practice link]]
====== Solutions ======
===== B. A Math Problem =====
**题目大意**：已知: $a+b=n$，求最小化 $lcm(a,b)$.
**题解**：
令 $d=gcd(a,b), m=lcm(a,b)$
由 $\ a\times b=d\times m,\ d|n$ 得到
$$m=\frac{a\times b}{d}=d\times a'\times b',\ a'+b'=\frac{n}{d}$$
固定 $d$，最小化 $m$ 得 $a'=1, b'=\frac{n}{d}-1$，进而
$$m=d\times b'=d\times(\frac{n}{d}-1)=n-d$$ $$b'=\frac{n}{d}-1>0\Rightarrow d