SOLUTION: 'I have a number of cupcakes. I can pack them in boxes which contain four cakes, three cakes or eight cakes. In each case I will fill all of the boxes with none left over. What is

The other tutor is right that you need the least common
multiple of 4,3,and 8.  It's the same as finding the 
least common denominator when adding fractions.

Here is an easy way to find the least common multiple,
or the least common denominator when adding fractions:

List them in a row

     4  3  8

Think of any PRIME number that will divide evenly into
one or more of them.  I thought of the PRIME number 2, 
for 2 will divide evenly into both the 4 and the 8.
So we put a vertical line and a 2 on the left.  We 
divide the 4 and the 8 by the 2, and put what we get,
2 and 4 underneath the 4 and 8.  Then we just bring down 
the 3, which 2 doesn't divide evenly into, like this:

    2|4  3  8
      2  3  4

Now think of a PRIME that will divide into at least
one of those 2,3,and 4.  I thought of 3, for 3 will 
divide evenly into the 3. So we put a vertical line 
and a 3 on the left.  We divide the 3 by the 3 getting 
1, and we put the 1 under the 3 and bring down the 2 
and the 4, which 3 doesn't divide evenly into, 
like this:

    2|4  3  8
    3|2  3  4
      2  1  4

Think of any PRIME number that will divide evenly into
one or more of them.  I thought of the PRIME number 2
again, for 2 will divide evenly into both the 2 and 
the 4. So we put a vertical line and a 2 on the left. 
We divide the 2 and the 4 by the 2 getting 1 and 2 and 
we put the 1 and 2 under them and bring down the 1, 
which 2 doesn't divide evenly into, like this:

    2|4  3  8
    3|2  3  4
    2|2  1  4 
      1  1  2

Now think of a PRIME that will divide into at least
one of those 1,1,and 1.  I thought of 2, for 2 will 
divide evenly into the 2. So we put a line as a
vertical line and a 2 on the left.  We 
divide the 2 by the 2 getting 1, and we put the 1
under the 2 and bring down the two 1's, 
which 2 doesn't divide evenly into, like this:    

    2|4  3  8
    3|2  3  4
    2|2  1  4 
    2|1  1  2
      1  1  1

Now we are done for we have only 1's on the bottom
Now multiply the PRIME numbers on the left of the
vertical lines:

2∙3∙2∙2 = 24.

That method will always give the LCM (least common
multiple).  You always must divide by a prime
number, and bring down the numbers that prime will
not divide into.  You are done when there are only
1's on the bottom.  Then you multiply together all
the prime numbers on the left.

Edwin