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(D) First,convert both lengths into millimeters:$10\, m\, 857\, mm = 10857\, mm$$15\, m\, 87\, mm = 15087\, mm$To get the least number of pieces,the l

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$184$

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(D) First,convert both lengths into millimeters:$10\, m\, 857\, mm = 10857\, mm$$15\, m\, 87\, mm = 15087\, mm$To get the least number of pieces,the length of each piece must be the greatest common divisor $(HCF)$ of the two lengths.Find the $HCF$ of $10857$ and $15087$:$10857 = 3 	imes 3619 = 3 	imes 77 	imes 47 = 141 	imes 77$$15087 = 3 	imes 5029 = 3 	imes 47 	imes 107 = 141 	imes 107$$HCF = 141\, mm$.The number of pieces from the first length $= 10857 \div 141 = 77$.The number of pieces from the second length $= 15087 \div 141 = 107$.Total number of pieces $= 77 + 107 = 184$.

What is the least number of cut pieces of equal length that can be cut out of two lengths $10\, m\, 857\, mm$ and $15\, m\, 87\, mm$?

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