Question

The length, breadth and height of a room are $825$ cm, $675$ cm and $450$ cm respectively Find the longest taps which can measure the three dimensions of the room exactly.

• A. $60$ cm
• B. $65$ cm
• C. $70$ cm
• D. $75$ cm

Answer 1

The correct option is D $75$ cm

Length = $825$ cm $=3\times 5\times 5\times 11$

Breadth = $675$ cm $=3\times 3\times 3\times 5\times 5$

Height = $450$ cm $=2\times 3\times 3\times 5\times 5$

Longest tape = HCF of $825$, $675$, and $450$ $=3\times 5\times 5=75cm$

Therefore, the longest tape is $75$ cm.