Answer: 18

100 = 50$\times$2$\times$1$\times$1     not all different
       = 10$\times$5$\times$2$\times$1     good! Sum = 18

Is there another way?
Factors of 100 not used: 4, 20, 25

100 = 4$\times$25$\times$1$\times$1     not all different
       = 4$\times$5$\times$5$\times$1       not all different. Cannot use 4
       = 25$\times$2$\times$2$\times$1     not all different. Cannot use 25
100 = 20$\times$5$\times$1$\times$1     not all different. Cannot use 20