This question from class 10 real numbers is very important.
I have been trying to solve it since last night but couldn’t do it.
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.
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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=2×2×2×2×2×2=2*6
Prime factorization of 80=2×2×2×2×5=2*4 ×5
Prime factorization of 96=2×2×2×2×2×3= 2*5 ×3
LCM == Product of highest power of each prime factor.
LCM =2*6×5×3=960cm
960 cm == 9.6 m.
the length of the rods is 64 cm, 80 cm and 96 cm.
thus the least length of the cloth that can be measured by an exact number of times is LCM of 64, 80 and 96.
64=2680=24×596=25×3
thus the LCM of 64, 80 and 96 is 26×3×5=960
thus the required length of the cloth is 960 cm = 9.6 m