Answer :

Least length of cloth that can be measured using this rod will be LCM of the three lengths.

So LCM of 64, 80 and 96 -

Prime factors of the given numbers are -

64 = 2 × 2 × 2 × 2 × 2 × 2

80 = 2 × 2 × 2 × 2 × 5

96 = 2 × 2 × 2 × 2 × 2 × 3

So LCM = product of prime factors with highest powers = 2^{6} × 3 × 5 = 960

∴ least length of cloth that can be measured using the rods = 960 cm = 9.6m

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