Question

Write the smallest composite number and find the LCM of the smallest prime number and the smallest composite number.

Answer 1

Hint: First we will find the smallest composite number, that is the smallest whole number which is divisible by at least three factors. After that we will find the smallest prime number, that is the smallest whole number that is divisible by only two factors. These two factors are one and the number itself.

Complete step-by-step answer:

To understand this problem, we will first define what is the whole number, composite number and prime number.

Whole number:

They are non-negative numbers (not fractions or rational numbers) including 0. In other words, whole numbers are a set of natural numbers including 0. Natural numbers are also called counting numbers. So, we can represent the set whole numbers as,

{whole numbers} = {natural numbers} + {0}

{whole numbers} = {1, 2, 3, 4, 5, 6, ........ $\infty $} + {0}

{whole numbers} = {0, 1, 2, 3, 4, 5, 6, ........... $\infty $}

Prime number:

Prime numbers are whole numbers which are divisible by one and the number itself. The prime numbers are:

{prime numbers} = {2, 3, 5, 7, 11, 13, 17.... etc.}

Here we can see that, the number 2 is divisible by only two numbers; they are 1 and the number 2 itself. Hence, 2 is a prime number. It is also the smallest prime number. The number 1 is not a prime number.

Composite number:

Composite numbers are whole numbers that have at least three factors. This means, a composite number is divisible by more than two numbers. In simple words a composite number has factors other than 1 and the number itself. The numbers 1 and 2 are not composite numbers.

The composite numbers are:

{composite numbers} = {4, 6, 8, 9, 10, 12.......}

Let us take number 4. The number 4 is divisible by 1, 2 and 4. Hence it is a composite number.

Similarly let us take number 6. The number 9 is divisible by 1, 2, 3 and 6. Hence, it is also a composite number.

 $\therefore $ the smallest composite number is 4.

Now, according to the question we have to find the L.C.M of the smallest prime number and the smallest composite number.

From the above definitions we observe that, the smallest prime number is 2 and the smallest composite number is 4. L.C.M of two numbers is defined as the least common multiple of the two numbers. Taking the LCM of 2 and 4 we get,

L.C.M (2, 4) = 4.

Hence, the smallest composite number is 2 and the L.C.M of the smallest prime number and the composite number is 4.

Note: Note that 1 is neither a prime nor a composite number. It should be noted that 2 is the smallest prime number. Also 2 is not a composite number, 4 is the smallest composite number.