Question

If L.C.M. of three numbers is 12 and the numbers are in the ratio of 1 : 2 : 3 then the numbers are 

(1) 2, 6, 12 

(2) 4, 8, 12 

(3) 5, 10, 15 

(4) 2, 4, 6

Answer 1

Correct option is (4) 2, 4, 6

Let the number be 'x'

Given the ratio 1 : 2 : 3

Hence, we can write the number to be x, 2x, 3x

HCF is x.

According to the question,

x + 2x + 3x = 12

6x = 12

x = \(\frac{12} {6}\)

x = 2

Thus, we get the numbers 

\(1 \times x = 1\times 2 = 2\)

\(2x = 2\times 2 = 4\)

\(3x = 3\times 2 = 6\)