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Three pieces of timber 42 m 49 m and 63 m long have to be divided into the planks of the same

length. what is the greatest possible length of each plank?



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There are 3 separate pieces of timber - they cannot be joined together to make planks.  We need to make many planks of equal length.  We do not want to waste any timber.

It we cut 42 m long timber from all the three pieces,  then there is no waste from the 1st one, there is a waste of 7m from 2nd timber and 21 m length is wasted from the third .    We get  3 planks of 42 m length.
If we take HCF of all the given lengths (42, 49, 63) , it is 7 m.  Hence we make planks of length 7m, then we get 6+7+9 = 22 planks of equal length 7 m.

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