Answer:
35 m
Explanation:
I will assume the goal is not to waste any wood. We need to find a common length that will allow each piece of wood to be divided into whole pieces with nothing left over. The shortest plank is 70 m, but that length will cause a loss of 35 m on the 105m plank, and also 35m on the 175m plank after two 70m sections have been cut off (175 - 140 = 35).
Looking at the actual lengths, one might spot that they are all evenly divisible by 35. See the table below. The numbers under "35" are the result of the length divided by 35. They are all whole numbers. We can cut each plank into 35m sections and have none left over.
Length (m) 35 (factor)
70 2 planks
105 3 planks
175 5 planks
This will result in 10 35m planks.
No need to plank me.