Mathematics · Time and Work

The team of A, B, and C was supposed to complete a piece of work. Working alone, A could have completed the same work in 190 hours, B in 285 hours, and C in 342 hours. The trio decided that only one of them would work at any point in time. In the first cycle of three days, A worked for 2 hours on Day 1, B worked for 2 hours on Day 2, and C worked for 2 hours on Day 3. In the second cycle of three days, A worked for 4 hours on Day 1, B worked for 4 hours on Day 2, and C worked for 4 hours on Day 3. In the third cycle of three days, A worked for 6 hours on Day 1, B worked for 6 hours on Day 2, and C worked for 6 hours on Day 3. This continued till the work was completed, with each working for 2n hours in Cycle n, the sole exception being made, if necessary, in the last cycle, as the work may get completed mid-cycle. What was the total number of days needed for the work to be completed?