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

Given :

The length of the given rods are  64 cm, 80 cm and 96 cm.

To find :

We have to find the least length of cloth that can be measured an exact number of times using any one of the above rods.

Solution :

The least common multiple of 64, 80, 96 is the required least length of the cloth.

Prime factorization of $64 = 2 \times 2\times 2\times 2\times 2\times 2 =2^6$

Prime factorization of $80 = 2 \times 2\times 2\times 2\times 5 = 2^4 \times 5$

Prime factorization of $96 = 2 \times 2\times 2\times 2\times 2\times3=2^5 \times 3$

LCM $=$ Product of highest power of each prime factor.

LCM $= 2^6 \times 5 \times 3 = 64 \times 15 = 960$

960 cm $=$ 9.6 m.

The required least length of the cloth is 9.6 cm.  

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Updated on: 10-Oct-2022

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