Three measuring rods are $64 c m, 80 c m a n d 96 c m$ 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

Solution:
Step 1: Find the least length of cloth by calculating L.C.M.:
Prime factors of $64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$
Prime factors of $80 = 2 \times 2 \times 2 \times 2 \times 5$
Prime factors of $96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3$
$∴ LCM (64, 80, 96) = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 5 = 960$
Step 2: Convert centimeter into meter:
$960 cm = 9.6 m [∵ 100 cm = 1 m]$
Final answer: Hence, the least length of the cloth required is $9.6 m$ .

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Three measuring rods are $64 c m, 80 c m a n d 96 c m$ 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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Three measuring rods are 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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Three measuring rods are $64 c m, 80 c m a n d 96 c m$ in length. Find the least length of cloth that can be measured an exact number of times, using any of the rods.