Calculate the value of HCF (8,9,25) `xx` LCM (8,9,25).

Options

A. 500
B. 1800
C. 200
D. 2500

Answer

To solve the problem of calculating the value of HCF (8, 9, 25) multiplied by LCM (8, 9, 25), we will follow these steps:

### Step 1: Calculate the HCF (Highest Common Factor) of 8, 9, and 25.

To find the HCF, we can list the factors of each number:

- Factors of 8: 1, 2, 4, 8
- Factors of 9: 1, 3, 9
- Factors of 25: 1, 5, 25

Now, we identify the common factors among these numbers. The only common factor is 1.

**HCF(8, 9, 25) = 1**

### Step 2: Calculate the LCM (Lowest Common Multiple) of 8, 9, and 25.

To find the LCM, we can use the prime factorization method:

- Prime factorization of 8: \(2^3\)
- Prime factorization of 9: \(3^2\)
- Prime factorization of 25: \(5^2\)

Now, we take the highest power of each prime number:

- For 2: \(2^3\)
- For 3: \(3^2\)
- For 5: \(5^2\)

Now, we multiply these together to find the LCM:

\[ \text{LCM} = 2^3 \times 3^2 \times 5^2 \]

Calculating this step-by-step:

1. Calculate \(2^3 = 8\)
2. Calculate \(3^2 = 9\)
3. Calculate \(5^2 = 25\)

Now multiply these results:

\[ \text{LCM} = 8 \times 9 \times 25 \]

Calculating \(8 \times 9 = 72\)

Now, calculate \(72 \times 25\):

\[ 72 \times 25 = 1800 \]

So, **LCM(8, 9, 25) = 1800**.

### Step 3: Calculate HCF(8, 9, 25) \(\times\) LCM(8, 9, 25).

Now we can multiply the HCF and LCM:

\[ \text{HCF} \times \text{LCM} = 1 \times 1800 = 1800 \]

### Final Answer:
\[ \text{HCF}(8, 9, 25) \times \text{LCM}(8, 9, 25) = 1800 \]

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