What is the smallest five-digit number that is exactly divisible by 12, 15 and 18?

First find LCM(12, 15, 18). With $12=2^2\times 3,15=3\times 5$ and $18=2\times 3^2$, the LCM is $2^2\times 3^2\times 5=180$. Now 10000 ÷ 180 = 55 remainder 100, so the first five-digit multiple is $56\times 180=10080$. Both 10260 $(=57\times 180)$ and 10800 $(=60\times 180)$ are also divisible by all three but are not the smallest, so they only catch a careless search.