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.

Home » 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.

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.

Answer:

Length of the three measuring rods are 64cm, 80cm and 96cm.

The length of cloth that can be measured an exact number of times = LCM (64, 80, 96)

Using prime factorization,

64 = 26

80 = 2⁴ × 5

96 = 2⁵ × 3

LCM = 26 × 3 × 5

LCM = 960cm

∴ LCM = 9.6m

The length of the cloth = 9.6m.