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Measurements of a room are 7m700cm,6m&3m75cm7\text{m}^{700\text{cm}},6\text{m} \& 3\text{m}75\text{cm}. And the length of the lingest rod that can measure all the three dimensions of the room.

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Q. Measurements of a room are 7m700cm,6m&3m75cm7\text{m}^{700\text{cm}},6\text{m} \& 3\text{m}75\text{cm}. And the length of the lingest rod that can measure all the three dimensions of the room.
  1. Convert to same unit: Convert all measurements to the same unit (centimeters). 7m=700cm7m = 700cm, 6m=600cm6m = 600cm, 3m75cm=375cm3m75cm = 375cm.
  2. Find greatest common divisor: Find the greatest common divisor (GCD) of 700 cm700\,\text{cm}, 600 cm600\,\text{cm}, and 375 cm375\,\text{cm}. Using the Euclidean algorithm: GCD(700,600)=100\text{GCD}(700, 600) = 100, GCD(100,375)=25\text{GCD}(100, 375) = 25.
  3. Calculate longest rod length: The GCD of 700700, 600600, and 375375 is 25 cm25\,\text{cm}, which is the length of the longest rod that can measure all three dimensions.

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