Given HCF of (16,100)=4 what is the LCM of (6,100)?

Options

A. 400
B. 398
C. 440
D. None

Answer

To find the LCM (Least Common Multiple) of the numbers 6 and 100, we can follow these steps:

### Step 1: Prime Factorization
First, we need to find the prime factorization of both numbers.

- **For 6**:
- 6 can be factored as \(2^1 \times 3^1\).

- **For 100**:
- 100 can be factored as \(2^2 \times 5^2\).

### Step 2: Identify the Highest Powers of Each Prime
Next, we need to identify the highest power of each prime number that appears in the factorizations.

- For the prime number **2**:
- The highest power is \(2^2\) (from 100).

- For the prime number **3**:
- The highest power is \(3^1\) (from 6).

- For the prime number **5**:
- The highest power is \(5^2\) (from 100).

### Step 3: Calculate the LCM
Now, we multiply these highest powers together to find the LCM.

\[ \text{LCM}(6, 100) = 2^2 \times 3^1 \times 5^2 \]

Calculating this step-by-step:

1. Calculate \(2^2 = 4\).
2. Calculate \(3^1 = 3\).
3. Calculate \(5^2 = 25\).

Now, multiply these results together:

\[ \text{LCM}(6, 100) = 4 \times 3 \times 25 \]

4. First, multiply \(4 \times 3 = 12\).
5. Then, multiply \(12 \times 25 = 300\).

Thus, the LCM of 6 and 100 is **300**.

### Final Answer
The LCM of (6, 100) is **300**.

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