A string can be cut equally into lengths of either 6cm or 8cm without any leftover. What is the shortest possible length of the string?

Question

Need answer with equations.

Answer 1

Possible lengths for the 6cm pieces include: 6, 12, 18, 24, 30, ...

These are all multiples of 6.

 

Likewise, the possible lengths for the 8cm pieces include: 8, 16, 24, 32, ...

These are all multiples of 8.

 

Notice that the smallest number that appears in both lists is 24.  This is your answer.

Mathematically, 24 is called the least common multiple.

 

Hope this helps.

 

Answer 2

You do not need equations; you need a LCM* answer--some number that is a multiple of both 6 & 8.

           

    *LCM = Least Common Multiple.

 

Answer: 24; do you see why?