To solve the problem of calculating the value of HCF (8, 9, 25) multiplied by LCM (8, 9, 25), we can follow these steps:
### Step 1: Find the Prime Factorization of Each Number
- **8** can be expressed as \(2^3\) (since \(8 = 2 \times 2 \times 2\)).
- **9** can be expressed as \(3^2\) (since \(9 = 3 \times 3\)).
- **25** can be expressed as \(5^2\) (since \(25 = 5 \times 5\)).
### Step 2: Determine the HCF (Highest Common Factor)
The HCF is found by taking the lowest power of all prime factors present in each number:
- The prime factors are \(2\), \(3\), and \(5\).
- The lowest powers of these factors in the numbers are:
- For \(2\): \(2^0\) (not present in 9 and 25)
- For \(3\): \(3^0\) (not present in 8 and 25)
- For \(5\): \(5^0\) (not present in 8 and 9)
Thus, the HCF is:
\[
HCF(8, 9, 25) = 2^0 \times 3^0 \times 5^0 = 1
\]
### Step 3: Determine the LCM (Lowest Common Multiple)
The LCM is found by taking the highest power of all prime factors present in any of the numbers:
- The prime factors are \(2\), \(3\), and \(5\).
- The highest powers of these factors in the numbers are:
- For \(2\): \(2^3\)
- For \(3\): \(3^2\)
- For \(5\): \(5^2\)
Thus, the LCM is:
\[
LCM(8, 9, 25) = 2^3 \times 3^2 \times 5^2
\]
Calculating this:
\[
= 8 \times 9 \times 25
\]
Calculating step-by-step:
- \(8 \times 9 = 72\)
- \(72 \times 25 = 1800\)
### Step 4: Calculate HCF multiplied by LCM
Now we multiply the HCF and LCM:
\[
HCF(8, 9, 25) \times LCM(8, 9, 25) = 1 \times 1800 = 1800
\]
### Final Answer
Thus, the final answer is:
\[
\text{HCF}(8, 9, 25) \times \text{LCM}(8, 9, 25) = 1800
\]
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