The band director was having a terrible time lining up his high school band for the Thanksgiving Day Parade. He didn’t have all that many kids, fewer than one hundred, but he couldn’t seem to arrange them on parade properly. He kept having odd numbers left over. He tried rows of five and there were four left over; he tried rows of six—four left over; rows of seven —one left over. He finally decided to have a very narrow parade and arranged them four abreast. That worked. What’s the smallest number of band members he could have had?
Edit: Come on people... show how you got there anyway.