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Lowest Common Multiple Application Word Problem

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Five children collect N pieces of Halloween candy and decide to split it evenly among them. When they try to divide it they have two pieces of candy left over. One of the children leaves, taking the 26 pieces of candy she collected with her. The remaining four children try to split the N-26 remaining pieces of candy and discover that they have one piece of candy left over. Frusterated, a second child leaves, taking 24 pieces of candy and the remaining three children split the N-26-24 pieces of candy left between them, delighted to discover that it can be split exactly three ways. What is the smallest (positive, of course) value for N for which this is possible? Are there other values of N for which this is possible also?

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Lowest common multiples are used to solve a word problem. The solution is detailed and well explained.

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(1) N=5k+2, because 2 candies left over if they try to divide N evenly among 5 of them
(2) N-26 = 4m+1, because 1 candies left over if they try to divide N-26 evenly among 4 of them
(3) N-26-24 = 3h, because ...

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