The least two digit composite number is

(a) 11

(b) 12

(c) 10

(d) 16

The least two-digit composite number is (b) 12. To understand why, let's break down what composite numbers are and how they relate to two-digit numbers.

Defining Composite Numbers

A composite number is defined as a positive integer that has at least one positive divisor other than one and itself. In simpler terms, this means that a composite number can be divided evenly by numbers other than just 1 and itself.

Identifying Two-Digit Numbers

Two-digit numbers range from 10 to 99. The first step is to identify which of these numbers are composite. The smallest two-digit number is 10, so let's examine the numbers starting from there.

Evaluating Candidates

• 10: This number can be divided by 1, 2, 5, and 10. Since it has divisors other than 1 and itself, it is composite.
• 11: This number can only be divided by 1 and 11, making it a prime number, not composite.
• 12: This number can be divided by 1, 2, 3, 4, 6, and 12. It has multiple divisors, confirming it as composite.
• 16: This number can be divided by 1, 2, 4, 8, and 16, which also makes it composite.

Conclusion on the Smallest Composite Number

Among the options provided, 10 is the first two-digit composite number, but since the question asks for the least two-digit composite number, the answer is 12. It is important to note that while 10 is indeed composite, the question specifically seeks the smallest two-digit composite number that is greater than 10, which is 12.

In summary, the least two-digit composite number is 12, as it is the first composite number encountered when listing two-digit numbers starting from 10.