Question

A box of marbles can be shared equally among 6, 7, or 8 students with 4 marbles left over each time. What is the least possible number of marbles in the box?

Answer 1

Let n is the number of marbles.
when marbles are equally shared among 6, 7 or 8 students, each time 4 marbles left over.
To find the least number of marbles, first we find out what is the smallest number that can be divided to 6, 7 and 8.
Now you see that 6 and 8 are divisible by 2 but 7 is non- divisible.
if we take LCM of 6, 7 and 8 and find the smallest number.
2 I6,7,8
   -------
    3,7,4
Now multiply 2,3,7 and 4
2 x 3 x7 x 4 = 168
each time 4 marbles left so
least possible number of marbles in the box = 168 + 4 = 172