What is the smallest five-digit number that is exactly divisible by 16, 24 and 40?

Explanation

1. 01

   The number must be a multiple of $\operatorname{LCM}(16, 24, 40) = 240$.

2. 02

   $10000 \div 240 = 41$ remainder 160, so the next multiple is $42 \times 240$.

3. 03

   $42 \times 240 = 10{,}080$.