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

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 = 26 × 3 × 5 = 960


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


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