Question 563995
The prime factorizations are
{{{125=5^3}}}
{{{235=5*47}}}
{{{270=2*5*3^3}}}
The numbers 2, 3, and 47 do not appear in all factorizations.
The only common factor is {{{5}}}. 
All three numbers are multiples of {{{5}}}, but not of {{{5^2}}}, or {{{5^3}}}.
So, the greatest common factor is 5.
The factorization of a common multiple must contain at least
{{{5^3}}}, {{{47}}}, {{{2}}}, and {{{3^3}}},
all prime factors with the largest exponents.
The least common multiple is
LCM={{{2*3^3*5^3*47}}}=317250
All the other common multiples are multiples of 317250.