Question

Length, Breadth and height of a cuboidal room are 5 m, 4 m and 3 m respectively, find the length of longest rod that can be kept inside the room

Answer 1

Length = 5 m = 500 cm
Breadth = 4m = 400 cm
Height = 3m = 300 cm
Using prime factorisation,
$500 = 5 \times 10 {}^{2}$
$400 = 4 \times 10 {}^{2}$
$300 = 3 \times 10 {}^{2}$
$hence \: hcf \: = 10 { }^{2} = 100$
Hence length of rod that can fit inside room is 100 cm or 1 m

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