If there are 3 rods of length 64 cm, 80 cm and 96 cm, then choose the option which gives the least length of cloth that can be measured an exact number of times, using any of the rods.

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900 cm

360 cm

960 cm

240 cm

answer is C.

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Detailed Solution

Given are 3 rods of length 64 cm, 80 cm and 96 cm.
We have to determine the least possible length of the cloth which can be measured an exact number of times by any of the given three rods. This means that such length of cloth will be represented by a whole number.
So, the length of the cloth will be the LCM of the lengths of the three rods as mentioned.
We proceed with the prime factorization of the given lengths of the three rods, i.e., 64, 80 and 96 as follows,

64 = 2 × 2 × 2 × 2 × 2 × 2 80 = 2 × 2 × 2 × 2 × 5 96 = 2 × 2 × 2 × 2 × 2 × 3

So, LCM (64, 80, 96)

= 26 × 3 × 5 = 960

Therefore, the least length of the cloth that can be measured an exact number of times, using any of the three rods is found to be 960 cm.
Hence, the correct option is (3).

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