Question

Find out the common multiples of \[5\] and \[6\]. Write the smallest multiple.

Answer 1

Hint:A multiple is the product of any quantity and an integer. For example, we can say that \[b\] is a multiple of \[a\] if \[b = na\], \[n\] is an integer called a multiplier. First, we will write the multiples of \[5\]and \[6\]. Then select the common multiples and out of that we will choose the smallest multiple.

Complete step by step solution:
Multiples of \[5\]: \[5,10,15,20,25,30,35,40,45,50,55,60......\]
These are found by multiplying \[5\] with integers such as \[1,2,3,4,5,6,7,8,9,10,11,12....\], that are called the multipliers.
Similarly, multiples of \[6\]: \[6,12,18,24,30,36,42,48,54,60,66,72,.....\]
These are found by multiplying \[6\] with integers such as \[1,2,3,4,5,6,7,8,9,10,11,12....\]
Now we will choose the common multiples. So, the common multiples of \[5\] and \[6\]are: \[30,60.....\]
Among these the smallest common multiple is: \[30\].
We can also find the smallest multiple directly by taking the LCM of \[5\] and \[6\]which is equal to:
\[5 \times 6 = 30\].
If we want to find more common multiples then we can find by listing more multiples of each and then taking out the common from them. But that will be a very lengthy process. In order to avoid this, we can take the first common multiple and then multiply that common multiple by integers to get a more common multiple.
For example, here the smallest common multiple is \[30\]. Now to find more common multiples we can multiply \[30\] by integers such as \[2,3,4,5,.....\]. The resulting numbers will be the common multiples of both \[5\] and \[6\].

Note:
One important point to note is that there is a difference between the factors and multiples of a number. Factors are the numbers by which the given number is completely divisible. Multiples of a number are the numbers which are completely divisible by the given number. Factors are always less than or equal to the given number whereas multiples are either equal or greater than the given number.