Question 1144398
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Add (mentally) one person to the band.


Then the number of persons is a multiple of 2, is a multiple of 5 and is a multiple of 7.


The smallest integer positive number with such properties is 2*5*7 = 70.


Now subtract (detach) this additional person, whom you added at the very beginning.


Thus you will get the <U>ANSWER</U> : least number of people in the marching band is 70-1 = 69.


<U>CHECK</U>.  69 is 1 short to be arranged in pairs;

           is 1 short to be arranged by 5s,

           and is 1 short to be arranged by 7s.
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Solved and completed.


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The tutor @greenestamps misread the problem and gave wrong answer.



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To see many other similar solved problems, look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/The-number-that-leaves-a-remainder-1-when-divided-by-2-by-3-by-4-by-5-and-so-on-until-9.lesson>The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9</A>

in this site.


The &nbsp;<U>Problem 2</U> &nbsp;of that lesson is an exact analogue to your problem in this post.