Question

Find the least length of a rope which can be cut into whole number of pieces of lengths 45 cm , 75 cm and 81 cm. ​

Answer 1

Solution :-

Given length of pieces - 45 cm, 75 cm and 81 cm

To find the length of the rope we have to find the L.C.M of 45 , 75 and 81

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3 | 45 , 75 , 81

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3 | 15 , 25 , 27

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3 | 5 , 25 , 9

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3 | 5 , 25 , 3

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5 | 5 , 25 , 1

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5. | 1 , 5 , 1

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| 1 , 1 , 1

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L.C.M = 3*3*3*3*5*5

= 2025 cm

So, the least no. of the rope should be 2025 cm which can be cut into whole number of pieces of length 45 cm , 75 cm and 81 cm

Answer 2

$\sf\huge\bold{Answer:}$

Given :

pieces of lengths 45 cm , 75 cm and 81 cm.

To find :

the least length of a rope which can be cut into whole number of pieces of lengths 45 cm , 75 cm and 81 cm.

i.e Least common factor for 45 , 75 and 81

Solution :

Least Common Factor (LCM) of 45,75,81 is

$\: | \: 45 - 75 - 81 \\ - - - - - - - \\3 | \: 15 - 25 - 27 \\ - - - - - - - \\3| \: \: \: \: \: \: 5 - 25 - 9 \\ - - - - - - - \\ 3| \: \: \: \: \: \: 5 - 25 - 3 \\ - - - - - - - \\ 3| \: \: \: \: \: \: 5 - 25 - 1 \\ - - - - - - - \\ 5|\: \: \: \: \: \: \: \: 1 - 5 - 1 \\ - - - - - - - \\ 5|\: \: \: \: \: \: \: \: 1 - 1 - 1$

LCM

$= {3}^{4} \times {5}^{2}$

$= 3 \times 3 \times 3 \times 3 \times 5 \times 5$

$= 9 \times 9 \times 25$

$= 81 \times 25$

$= 2025 m$

⟶the least length of a rope which can be cut into whole number of pieces of lengths 45 cm , 75 cm and 81 cm is 2025 metres.