13. What is the minimum number of cubes of the same size required to fill a box with dimensions $30 \mathrm{~cm}$ by $40 \mathrm{~cm}$ by $50 \mathrm{~cm}$ ?
A 20
B 40
C 60
D 80
E 120
13. C To fill the box, the side-length of the cube needs to divide exactly into the length, width and height of the box. To obtain the minimum number of cubes to fill the box, we need this side-length to be as large as possible. Therefore we need this side-length, in $\mathrm{cm}$, to be the highest common factor of 30,40 and 50 , which is 10 . Hence with cubes of side-length $10 \mathrm{~cm}$, we get the minimum to fill the box. Therefore the minimum number of cubes required is $(30 \div 10) \times(40 \div 10) \times(50 \div 10)=3 \times 4 \times 5=60$.