Suppose in chinese reminder theorem all residue are the same. $$x \equiv a \mod m_1\\ x \equiv a \mod m_2\\ x \equiv a \mod m_3\\ ...\\ x \equiv a \mod m_n$$
Does it mean $ x \equiv a \mod lcm(m_1,m_2,..,m_n)$?
If not, in which cases does?
For exampe if
$$x = -1 \mod 2\\
x \equiv -1 \mod 3\\
x \equiv -1 \mod 4\\
x \equiv -1 \mod 5\\
x \equiv -1 \mod 6\\
$$
concludes $x \equiv -1 \mod 60$