# 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,

Question:

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.

Solution:

Length of the three measuring rods are 64 cm, 80 cm and 96 cm, respectively.
∴ Length of cloth that can be measured an exact number of times = LCM (64, 80, 96)
Prime factorisation:

$64=2^{6}$

$80=2^{4} \times 5$

$96=2^{5} \times 3$

$\therefore$ LCM $=$ Product of greatest power of each prime factor involved in the numbers $=2^{6} \times 3 \times 5=960 \mathrm{~cm}=9.6 \mathrm{~m}$

Hence, the required length of cloth is 9.6 m.