Question

Write the first ten multiples of \[6\] and \[8\]. Find their common multiples.

Answer 1

Hint: In the given problem, we have to write the first ten multiples of \[6\] and \[8\]. The multiples of a particular number are the numbers that can be divided by the given number without leaving any remainder. For example, every even number is the multiple of \[2\] as it divides the given number completely. Now, after finding the multiples of \[6\] and \[8\], we will select the common multiples.

Complete answer:
 Step 1: Writing down the first ten multiples of \[6\], that are:
\[6,12,18,24,30,36,42,48,54,60\]
Step 2: Writing down the first ten multiples of \[8\], that are:
\[8,16,24,32,40,48,56,64,72,80\]
Step 3: We will select the common multiples, i.e., the numbers that are the multiples of both \[6\] and \[8\]. Hence, the numbers are \[24\] and \[48\].

Hence, we selected the numbers \[24\] and \[48\] in step 1 and step 2.

Note: The common multiples of two or more numbers are the numbers which divide the particular numbers completely, at the same time, leaving no remainder behind.
The common multiples of any two numbers are the multiples of the L.C.M. i.e., the least common multiple of both of these numbers. For example, in the given question, the least common multiple i.e., L.C.M. of \[6\] and \[8\] is \[24\]. Hence, the multiples of \[24\] which are \[24\] and \[48\] in the given problem will be the common multiples of \[6\] and \[8\]. Hence, we selected \[24\] and \[48\]. Another multiple of \[24\] which is present in the first ten multiples of \[8\] is \[72\] but it is not present in the first ten multiples of \[6\].
Hence, the common multiples of \[6\] and \[8\] in the given problems are \[24\] and \[48\].