Question

the Length breadth and height of a room are 12 15 and 18 respectively determine the length of longest streak that can measure all the dimensions on the room in exact number of times?​

Answer 1

$\red{\textbf{Answer :- 3m}}$

Step-by-step explanation:

$\red{\textbf{Given :-}}$

$\textsf{length = 12}$

$\textsf{breadth = 15}$

$\textsf{height = 18}$

$the \: longest \: length \: of \: streak \: that \: can \:$

$measure \:all \: the \: dimensions \: of \: the \: room \: \\ is \: the$

$Highest \: common \: factor(HCF) \: of \: \\ its \: length,$$breadth \: and \: height \: .$

$Now,$

$HCF \: of \: 12 \: 15 \: and \: 18$

$prime \: factorization \: of \: 12 = 3 \times 2 \times 2$

$prime \: factorization \: of \: 15 = 3 \times 5$

$prime \: factorization \: of \: 18 = 3 \times 3 \times 2$

$HCF = 3$

$the \: length \: of \: longest \: streak \: that \: measure \: all$

$the \: dimensions \: of \: the \: rooms \: in \: exact \:$

$number \: of \: times \: \: is \: \: 3m$