Question

Three measuring rods 64 cm, 80 cm and 96 cm in length. Find the least length of cloth that can be measured exact number of times using anyone of the above rods.

Answer 1

Lengths of three measuring rods = 64 cm, 80 cm and 96 cm

Least Length of cloth that can be measured = LCM (64, 80, 96)

64 = 2⁶

80 = 2³ × 3 × 5

96 = 2⁵ × 3

So, 2⁶ × 3 × 5 are the greatest powers of the prime factors 2, 3 and 5

LCM (64, 80, 96) = 2⁶ × 3 × 5 = 960

Least Length of cloth that can be measured is 960 cm