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

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


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    Solution:

    Three measuring rods 64 cm, 80 cm and 96 cm in length. The least length of cloth that can be measured exact number of times using anyone of the above rods is 960 cm.
    Given three measuring rods are 64 cm, 80 cm and 96 cm in length respectively.
    Prime factorization of 64, 80 and 96 is,
    Prime factors are,
    64= 2 6   80= 2 3 × 3 1 × 5 1   96= 2 6 × 3 1   The L.C.M of 64, 80, 96 is,
    ⇒ 2 6 × 3 1 × 5 1  
    ⇒2×2×2×2×2×2×3×5  
    ⇒   960
    Hence, the least length is 960 cm.
     
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