Questions & Answers

Question

Answers

A. 2, 6, 12

B. 4, 8, 12

C. 5, 10, 15

D. 2, 4, 6

Answer
Verified

In this question first, assume the common factor to be\[x\], then find the numbers by equating it to the given LCM.

Since the number whose LCM is given in the ratio of 1:2:3 hence we can write the number to be $x,2x,3x$.

Now find the factor of each number as:

\[

1x = 1 \times x \\

2x = 2 \times x \\

3x = 3 \times x \\

\]

So the LCM of the three numbers will be:

\[LCM\left( {1x,2x,3x} \right) = 1 \times 2 \times 3 \times x = 6x\]

Hence the LCM of numbers \[1x,2x,3x\] is \[6x\].

Also given the LCM of the original numbers is 12, now equate the LCM as

\[

6x = 12 \\

x = \dfrac{{12}}{6} \\

= 2 \\

\]

Hence the value of\[x = 2\], now find the numbers by putting the value of $x$ in the ratios as:

\[

1x = 1 \times 2 = 2 \\

2x = 2 \times 2 = 4 \\

3x = 3 \times 2 = 6 \\

\]

Hence the numbers whose LCM is 12 are 2,4,6

Option D is correct.

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