Question

Find the largest four digit number which when reduced by $54$ is perfectly divisible by all even natural numbers less than $20$.

Answer 1

Even natural numbers less than 20 are $2,4,6,8,10,12,14,16,18$
Their LCM $=2\times LCM$ of first 9 natural numbers $=2\times 2520=5040$.
This happens to be the largest four-digit number divisible by all even natural numbers less than $20$.
$54$ was subtracted from our required number to get this number.
Hence, the required number $-54=5040$.
$\Rightarrow$ Required number $=5094$