Question

Paul has 3 pieces of rope of length 36cm,40cm,and 48cm respectively. He needs to select 2 out of the 3 pieces and cut them into smaller pieces of equal length. What is the greatest possible length of each smaller piece if there is to be no wastage?

Answer 1

why wouldn't he take the longest two, cut them into 36cm pieces?

Answer 2

I'd say it's because they are to be cut from 2 of the pieces. That is, which two ropes have the largest common factor?

36 = 12*3
40 = 8*5
48 = 12*4

Looks to me like 12cm is the longest piece that divides evenly 2 of the 3 original lengths.