A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In how many days all three together can do the work ?

In these kind of questions, always take total work as L.C.M. of number of days.
Here L.C.M. of Total Work = 360
One day work of A + B = $$\frac{{360}}{{72}}$$  = 5 unit/day
One day work of B + C = $$\frac{{360}}{{120}}$$  = 3 unit/day
One day work of C + A = $$\frac{{360}}{{90}}$$  = 4 unit/day
∴ Total units/day = 5 + 3 + 4 = 12
(Here , 12 unit represents twice of the work done by A, B and C. So we will divide it by 2)
Work done by (A + B + C) per day = $$\frac{{12}}{2}$$ = 6 units/day
∴Total time taken by (A + B + C)
$$\eqalign{ & = \frac{{360}}{6} \cr & = 60{\text{ days}} \cr} $$