Question : The LCM and ratio of the three numbers are 1386 and 3 : 7 : 11, respectively. The sum of the greatest and least numbers is:
Option 1: 60
Option 2: 64
Option 3: 84
Option 4: 108
Correct Answer: 84
Solution :
The LCM and ratio of the three numbers = 1386
Let the numbers be $3x, 7x,$ and $11x$.
According to the question:
$(3\times7\times11)x=1386$
⇒ $231x=1386$
$\therefore x=6$
Thus, Least number $= 3x=3\times6=18$
Greatest number $=11x=11\times6=66$
$\therefore$ Sum $=18+66=84$
Hence, the correct answer is 84.
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