The length,breadth,and height of a prayer roo | vedclass

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Question

(C) To find the longest rod that can measure the three dimensions ($15\,m$,$12\,m$,and $21\,m$) exactly,we need to calculate the Highest Common Factor

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) To find the longest rod that can measure the three dimensions ($15\,m$,$12\,m$,and $21\,m$) exactly,we need to calculate the Highest Common Factor $(HCF)$ of these three numbers.Step $1$: Find the prime factorization of each dimension:$15 = 3 	imes 5$$12 = 2^2 	imes 3$$21 = 3 	imes 7$Step $2$: Identify the common prime factors.The only common prime factor among $15$,$12$,and $21$ is $3$.Step $3$: The $HCF$ is the product of the lowest powers of common prime factors.$HCF(15, 12, 21) = 3$.Therefore,the longest rod that can measure the dimensions exactly is $3\,m$.

The length,breadth,and height of a prayer room are $15\,m$,$12\,m$,and $21\,m$ respectively. Determine the longest rod which can measure the three dimensions of the room exactly. (in $,m$)

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