<PRE><B>Question 56530</B>
A bag contains 100 marbles. The marbles can be divided into equal shares among 6,7 or 8 children with 1 marble left over each time. What is the least number of marbles that the box can contain?
LET NUMBER OF MARBLES = N
SINCE N LEAVES THE SAME REMAINDER OF 1 WHEN DIVIDED WITH 6,7,8...FIND LCM OF 6,7&amp;8 AND ADD 1 TO IT TO GET MINIMUM VALUE FOR N
2|6,7,8
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  3,7,4
SO LCM = 2*3*7*4 = 168
N = 168+1 = 169 IS THE MINIMUM NUMBER OF MARBLES NEEDED. 
 
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