Question

Given that the dimensions of a room are $8m10cm$ and $6m30cm$ and $5m40cm$, find the length of the longest rod in cm, which can measure these dimensions exactly.

Answer 1

Length $=8m10cm=810cm$

Breadth $=6m30cm=630cm$

Height $=5m40cm=540cm$

HCF of 810, 630, 540 :-

$810=2\times 3\times 3\times 3\times 3\times 5$

$630=2\times 3\times 3\times 5\times 7$

$540=2\times 2\times 3\times 3\times 3\times 5$

$HCF=2\times 3\times 3\times 5=90$

Therefore, length of longest rod which can measure the three dimensions exactly is $90cm$.