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posted by ssssss .
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?

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

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.
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