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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?

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

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    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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