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
The smallest two-digit number is 10. To check if it's composite, we need to see if it has divisors other than 1 and itself.
- 10 can be divided by 1, 2, 5, and 10.
Since it has divisors other than 1 and itself, **10 is a composite number**.

### Step 2: Identify the smallest composite number
The smallest natural number is 1, but it is neither prime nor composite.
- The next number is 2, which is a prime number.
- The next number is 3, which is also a prime number.
- The next number is 4.
Since 4 can be divided by 1, 2, and 4, it has divisors other than 1 and itself, making **4 the smallest composite number**.

### Step 3: Find the LCM of 10 and 4
To find the LCM (Least Common Multiple), we can use the prime factorization method.

1. **Prime factorization of 10**:
- 10 = 2 × 5

2. **Prime factorization of 4**:
- 4 = 2 × 2 = 2²

3. **Identify the highest power of each prime factor**:
- For 2: the highest power is 2² (from 4)
- For 5: the highest power is 5¹ (from 10)

4. **Multiply these together**:
- LCM = 2² × 5¹ = 4 × 5 = 20

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

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