Question

Find the H.C.F, if the numbers are in the ratio of 4 : 5 : 6 and their L.C.M. is 2400.

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

$\rm \red{Given}$

$\rm{numbers \: are \: in \: the \: ratio = \: 4 : 5 : 6 }$

$\rm \red{Let}$

$\rm{the \: numbers \: be \: as \: 4x, \: 5x \: \: and \: 6x}$

$\rm{L.C.M \: of \: these \: numbers \: = 60x}$

$\rm \red{From \: the \: Question}$

$\rm{L.C.M \: of \: these \: numbers \: = 2400}$

$\rm \implies \: 60x = 2400$

$\rm \implies \: x = \dfrac{2400}{60}$

$\implies \rm{x = 40}$

$\rm \red{Then \: the \: numbers \: are : }$

$\rm4x = 4 \times 40 = 160 \\ \rm5x = 5 \times 40 = 200 \\ \rm 6x = 6 \times 40 = 240$

$\rm{H.C.F \: of \: 160, \: 200, \: 240 \: is \: 40}$