South African Mathematics Olympiad First Round

If all terms are brought to $60$, the least common multiple (LCM), then all the numerators except $6$ have a factor $5$. Since the required numerator is $60$, which also has a factor $5$, the term that must be dropped is $\frac{1}{10}$.

Alternatively, $$\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{10}+\frac{1}{12}=\frac{30+15+10+6+5}{60}=\frac{66}{60}=1+\frac{1}{10}.$$