The LCM of smallest two digit composite number and smallest composite number is

Options

A. `12`
B. `4`
C. `20`
D. `44`

Explanation

To find the LCM of the smallest two-digit composite number and the smallest composite number, we will follow these steps:

### Step 1: Identify the smallest two-digit composite number and the smallest composite number.
- The smallest two-digit composite number is **10**.
- The smallest composite number is **4**.

### Step 2: Factorize both numbers.
- The prime factorization of **4** is:
\[ 4 = 2 \times 2 = 2^2 \]
- The prime factorization of **10** is:
\[ 10 = 2 \times 5 \]

### Step 3: Determine the LCM using the highest powers of the prime factors.
- The prime factors we have are **2** and **5**.
- From the factorization:
- For **2**, the highest power is \(2^2\) (from 4).
- For **5**, the highest power is \(5^1\) (from 10).

Thus, the LCM is calculated as:
\[ \text{LCM} = 2^2 \times 5^1 \]

### Step 4: Calculate the LCM.
- Now, we compute:
\[ 2^2 = 4 \]
\[ 5^1 = 5 \]
\[ \text{LCM} = 4 \times 5 = 20 \]

### Conclusion:
The LCM of the smallest two-digit composite number (10) and the smallest composite number (4) is **20**.