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Smallest multiple beyond 2010 with terminating decimals

Middle school · ●●○○○ 20 pts

Let SS be the set of all integers kk such that 17k66\frac{17k}{66} and 13k105\frac{13k}{105} are both terminating decimals. What is the smallest integer in SS that is greater than 2010?

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terminating decimalsprime factorisationleast common multiple