S alone can do a piece of work in 14 days. T alone can do the same work in 21 days. U alone can do the same work in 28 days. Working together, in how many days will they complete the work?

LCM of 14, 21 and 28 is 84.

Let's assume the total work is 84 units.

S alone can do a piece of work in 14 days.

Efficiency of S = $$\frac{84}{14}$$ = 6 units/day

T alone can do the same work in 21 days.

Efficiency of T = $$\frac{84}{21}$$ = 4 units/day

U alone can do the same work in 28 days.

Efficiency of U = $$\frac{84}{28}$$ = 3 units/day

Time taken by all of them working together to complete the work = $$\frac{84}{6+4+3}$$

= $$\frac{84}{13}$$ days