Problem E

Number Crunching

While waiting for the bus one day, Leo divided numbers on his calculator. He noticed that when \(44\,000\) is divided by \(18\), the remainder is \(8\). He then noticed that the remainder is also \(8\) when \(44\,000\) is divided by \(24\), and also when \(44\,000\) is divided by \(39\). Leo then set out to find other numbers that had the same remainder (not necessarily \(8\)), when divided by \(18,~24,\) and \(39\).

How many five-digit positive integers have the same remainder when divided by \(18,~24,\) and \(39\)?