Question

What are the three common multiples of 18 and 6?
A. 18,6,9
B. 18,36,6
C. 36,54,72
D. None of these

Answer 1

Hint: In order to check the common multiple of both the numbers from the given options, check separately for the divisibility of each of the numbers. Since the options are very close to a small integral multiple , so selection on the basis of multiple can be done.

Complete Step-by-Step solution:
The numbers are 18 and 6.
The multiples of 18 are given as $18 \times n$ , where n is the natural number. So the multiples of 18 are:
$
  18 \times 1 = 18 \\
  18 \times 2 = 36 \\
  18 \times 3 = 54 \\
  18 \times 4 = 72 \\
  18 \times 5 = 90 \\
 $
Similarly the multiples of 6 is given as $6 \times n$ , where n is the natural number. So the multiples of 6 are:
\[
  6 \times 1 = 6 \\
  6 \times 2 = 12 \\
  6 \times 3 = 18 \\
  6 \times 4 = 24 \\
  6 \times 5 = 30 \\
  6 \times 6 = 36 \\
  ...... \\
  6 \times 9 = 54 \\
  ...... \\
  6 \times 12 = 72 \\
 \]
Hence, by the observation it is clear that 36, 54, 72 is the multiple of both 6 and 18.
So, option C is the correct option.

Note: This problem can also be done by the method of LCM. As we know that any number which is the multiple of 2 different numbers is always the multiple of its LCM. So we could have found out the LCM and would have checked for the divisibility with the LCM.