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Question Number 55476 by pooja24 last updated on 25/Feb/19

4 metal rods of length 78 cm,104 cm,117cm,  a.nd 169 cm are to be cut into parts of equal length  Each length must be as long as possible  What is the maximum number of pieces  that can be cut?

$$\mathrm{4}\:{metal}\:{rods}\:{of}\:{length}\:\mathrm{78}\:{cm},\mathrm{104}\:{cm},\mathrm{117}{cm}, \\ $$$${a}.{nd}\:\mathrm{169}\:{cm}\:{are}\:{to}\:{be}\:{cut}\:{into}\:{parts}\:{of}\:{equal}\:{length} \\ $$$${Each}\:{length}\:{must}\:{be}\:{as}\:{long}\:{as}\:{possible} \\ $$$${What}\:{is}\:{the}\:{maximum}\:{number}\:{of}\:{pieces} \\ $$$${that}\:{can}\:{be}\:{cut}? \\ $$

Answered by Joel578 last updated on 25/Feb/19

GCD(78, 104, 117,169) = 13  Number of pieces = ((78)/(13)) + ((104)/(13)) + ((117)/(13)) + ((169)/(13)) = 36

$$\mathrm{GCD}\left(\mathrm{78},\:\mathrm{104},\:\mathrm{117},\mathrm{169}\right)\:=\:\mathrm{13} \\ $$$$\mathrm{Number}\:\mathrm{of}\:\mathrm{pieces}\:=\:\frac{\mathrm{78}}{\mathrm{13}}\:+\:\frac{\mathrm{104}}{\mathrm{13}}\:+\:\frac{\mathrm{117}}{\mathrm{13}}\:+\:\frac{\mathrm{169}}{\mathrm{13}}\:=\:\mathrm{36} \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 25/Feb/19

excellent...confidance enhance determination...

$${excellent}...{confidance}\:{enhance}\:{determination}... \\ $$

Commented by Joel578 last updated on 25/Feb/19

thanks sir

$${thanks}\:{sir} \\ $$

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