Question

What is the sum of the first and second common multiples of $4$ and $6$?
A. $36$
B. $144$
C. $72$
D. $288$

Answer 1

Hint: A common multiple is a multiple common between two numbers. To find the sum of common multiples, first, we will have to find the multiples of both the numbers, and then we will find the first and second common multiples from the list of multiples and then add it, so as to get the final answer.

Complete step by step answer:
The two numbers given in the question are $4$ and $6$.
The multiples of $4$ are as follows : $4,8,12,16,20,24,28,32,36,40,44,48,...$
The multiples of $6$ are as follows : $6,12,18,24,30,36,42,48,54,60,66,72,...$
The first common multiple of $4$ and $6$ is $12$.
The second common multiple of $4$ and $6$ is $24$.
The sum of the first and second common multiples of $4$ and $6$ = $12 + 24 = 36$ .
Therefore, the sum of the first and second common multiples of $4$ and $6$ is $36$.

Hence, the correct answer is option $A.$

Note: A common multiple is a whole number that is a shared multiple of each set of numbers. The multiples that are common to two or more numbers are called the common multiples of those numbers. A number can have an infinite number of multiples. Therefore, any two numbers or set of numbers can have an infinite number of common multiples. The smallest common multiple of two or more numbers is called their Least Common Multiple (LCM).