Question

A box contains over 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?

Answer 1

LET NUMBER OF MARBLES = X

SINCE N LEAVES THE SAME REMAINDER OF 1 WHEN DIVIDED WITH 6,7,8...

FIND LCM OF 6,7&8 AND ADD Remainder TO IT TO GET MINIMUM VALUE FOR N

LCM of 6,7,8 = 168


So least. number of marbles in the box is
168 + 1=169
$169$