Question

What is the least positive integer that is the product of $3$ different prime numbers greater than $2?$
A. $27$
B. $45$
C. $63$
D. $75$
E. $105$

Answer 1

Hint: Prime numbers can be defined as the number which has only two factors and the factors are one and the number itself. First of all find the least three prime numbers and then will find its product for the resultant required value.

Complete step by step answer:
 Prime factorization can be expressed as the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are defined as the numbers greater than $1$ and which are not the product of any two smaller natural numbers. For Example: $2,{\text{ 3, 5, 7,}}......$ $2$ is the prime number as it can have only $1$ factor.

The three least prime numbers greater than $2$are $3,5,7$
The product of these prime numbers are $3 \times 5 \times 7 = 105$

So, the correct answer is “Option E”.

Note: Be good finding the prime factorization for the given term. Prime factorization can be found by using other methods such as the factor tree method. Know the difference between the prime numbers and the composite numbers. Composite numbers are defined as the product of prime numbers having more than two factors. To get the factors be good in multiples and remember it at least twenty.