The L.C.M of the smallest 2 digit composite number and the smallest composite number is:

• (a) 12
• (b) 4
• (c) 20
• (d) 44

To find the least common multiple (LCM) of the smallest two-digit composite number and the smallest composite number, we first need to identify these numbers. Let's break it down step by step.

Identifying the Numbers

The smallest composite number is 4. A composite number is defined as a positive integer that has at least one positive divisor other than one or itself. The number 4 meets this criterion because it can be divided by 1, 2, and 4.

Next, we look for the smallest two-digit composite number. The smallest two-digit number is 10, and it is composite because it can be divided by 1, 2, 5, and 10. Therefore, the smallest two-digit composite number is 10.

Finding the LCM

Now that we have our two numbers, 4 and 10, we can calculate the LCM. The LCM of two numbers is the smallest number that is a multiple of both. There are several methods to find the LCM, but one straightforward way is to use the prime factorization method.

Prime Factorization

• The prime factorization of 4 is: 2 × 2 or 2².
• The prime factorization of 10 is: 2 × 5.

To find the LCM, we take the highest power of each prime number that appears in the factorizations:

• From 4, we take 2².
• From 10, we take 5¹.

Now, we multiply these together to find the LCM:

LCM = 2² × 5¹ = 4 × 5 = 20

Final Answer

Thus, the LCM of the smallest two-digit composite number (10) and the smallest composite number (4) is 20. Therefore, the correct option is (c) 20.