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Three numbers are in the ratio 2:3:4, If their LCM is 240 the smaller of the three numbers is = ?

140
260
330
480

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let number are \\ = 2 x, 3 x, 4 x \\ given, \\ LCM of (2 \times 3 \times 2) x = 12 x \\ 12 x = 240 \\ x = 20 \\ ∴ numbers are 2 \times 20 =  40 \\ 3 \times 20 = 60 \\ 4 \times 20 = 80 \\ ∴ Smaller is 40 \end{aligned}

$\eqalign{ & {\text{Let number are}} \cr & {\text{ = }}2x,3x,4x \cr & {\text{given,}} \cr & {\text{LCM of }}\left( {2 \times 3 \times 2} \right)x = 12x \cr & 12x = 240 \cr & x = 20 \cr & \therefore {\text{numbers are 2}} \times {\text{20 = 40}} \cr & {\text{3}} \times 20 = 60 \cr & {\text{4}} \times 20 = 80 \cr & \therefore {\text{Smaller is 40}} \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Let number are \\ = 2 x, 3 x, 4 x \\ given, \\ LCM of (2 \times 3 \times 2) x = 12 x \\ 12 x = 240 \\ x = 20 \\ ∴ numbers are 2 \times 20 =  40 \\ 3 \times 20 = 60 \\ 4 \times 20 = 80 \\ ∴ Smaller is 40 \end{aligned}

$\eqalign{ & {\text{Let number are}} \cr & {\text{ = }}2x,3x,4x \cr & {\text{given,}} \cr & {\text{LCM of }}\left( {2 \times 3 \times 2} \right)x = 12x \cr & 12x = 240 \cr & x = 20 \cr & \therefore {\text{numbers are 2}} \times {\text{20 = 40}} \cr & {\text{3}} \times 20 = 60 \cr & {\text{4}} \times 20 = 80 \cr & \therefore {\text{Smaller is 40}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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