Three measuring rods is 64 cm, 80 cm and 96 cm in length. Find the least length of cloth that can be measured an exact number of times, using any of the rods.

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Solution

the length of the rods is 64 cm, 80 cm and 96 cm.

thus the least length of the cloth that can be measured by an exact number of times is LCM of 64, 80 and 96.

$64 = 2^{6} 80 = 2^{4} \times 5 96 = 2^{5} \times 3$

thus the LCM of 64, 80 and 96 is $2^{6} \times 3 \times 5 = 960$

thus the required length of the cloth is 960 cm = 9.6 m

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Three measuring rods is 64 cm, 80 cm and 96 cm in length. Find the least length of cloth that can be measured an exact number of times, using any of the rods.

the length of the rods is 64 cm, 80 cm and 96 cm. thus the least length of the cloth that can be measured by an exact number of times is LCM of 64, 80 and 96. 64=2680=24×596=25×3 thus the LCM of 64, 80 and 96 is 26×3×5=960 thus the required length of the cloth is 960 cm = 9.6 m