Question

Find the first four common multiples of the following: $ 3{\text{ and 4}} $
 $
  A.\,{\text{24,28,32,36}} \\
  {\text{B}}{\text{. 24,27,33,36}} \\
  {\text{C}}{\text{. 12,24,36,48}} \\
  {\text{D}}{\text{. 12,15,20,24}} \\
  $

Answer 1

Hint: Multiples are obtained by multiplying the number by the integers. In other words, the multiples of the number are all the numbers that are products of the number and any other natural numbers. For Example – the multiples of $ 2 $ are $ 2,{\text{ 4, 6, 8, 10, 12, 14 , 16}} $ and so on... For the multiple of $ 3\;{\text{and 4}} $ , we will first find its LCM and then the multiples of the resultant number.

Complete step-by-step answer:
Now the LCM (Least common multiple) of $ 3\,{\text{and 4}} $ is $ 12. $
(Since in $ 3{\text{ and 4}} $ , there are no common factor so we directly multiply $ 3 \times 4 = 12 $ )
The get the first four multiples of $ 12 $
The first multiple of $ 12 $ is-
$\Rightarrow$ Multiply $ 12 $ by $ 1 = {\text{12}} \times {\text{1 = 12}} $
Similarly to get the second multiple of $ 12 $ ,
$\Rightarrow$ Multiply $ 12 $ by $ 2\;{\text{ = 12}} \times {\text{2 = 24}} $
In the same way we can find the third, fourth, fifth and sixth multiples by multiplying $ 12 $ with $ 3{\text{ and 4}} $ respectively.
$\Rightarrow$ Third multiple of $ 12 $ is $ = {\text{ 12}} \times {\text{3 = 36}} $
$\Rightarrow$ Fourth multiple of $ 12 $ is $ = {\text{12}} \times {\text{4 = 48}} $
Therefore, the first four multiples of $ 3\,{\text{and 4 are 12,24,36,48}} $

So, the correct answer is “Option C”.

Note: A multiple is the resultant of multiplying a number by an integer and never by the fractions. Multiples of the numbers are infinite; there is no end for the multiples of any number. Always remember that the first multiple of any number is the number itself. Every number is the multiple of $ 1 $ . Also, $ 0 $ (zero) is the multiple of every number. Actually, the multiples are the numbers which you learn in the form of the tables generally till the tenth or twelfth place of every number. When a number is the multiple of $ 2 $ or more numbers then it is called the common multiple of that number.