\(5+5^2+5^3+...+5^{58}+5^{60}\)

=\(\left(5^{60}+5^{59}\right)+...+\left(5^4+5^3\right)+\left(5^2+5\right)\)

=\(5^{59}.\left(5^0+5\right)+...+5^3.\left(5^0+5\right)+5.\left(5^0+5\right)\)

=\(5^{59}.6+...+5^3.6+5.6\)

\(\Rightarrow5+5^2+5^3+...+5^{60}⋮6\)

\(\Rightarrow dpcm\)

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