HCF and LCM of `a^(2)b^(3)c^(4)` and `a^(5)b^(4)c^(3)` are :

Options

A. `a^(2)b^(3)c^(3), a^(5)b^(4)c^(3)`
B. `a^(2)b^(2)c^(3),a^(2)b^(3)c^(4)`
C. `a^(2)b^(3)c^(3), a^(5)b^(4)c^(4)`
D. `a^(5)b^(3)c^(3),a^(5)b^(4)c^(3)`

Answer

To find the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of the expressions \( a^2b^3c^4 \) and \( a^5b^4c^3 \), we will follow these steps:

### Step 1: Identify the powers of each variable in both expressions
- For the first expression \( a^2b^3c^4 \):
- Power of \( a \) = 2
- Power of \( b \) = 3
- Power of \( c \) = 4

- For the second expression \( a^5b^4c^3 \):
- Power of \( a \) = 5
- Power of \( b \) = 4
- Power of \( c \) = 3

### Step 2: Calculate the HCF
The HCF is found by taking the lowest power of each variable from both expressions.

- For \( a \): The lowest power is \( \min(2, 5) = 2 \), so we have \( a^2 \).
- For \( b \): The lowest power is \( \min(3, 4) = 3 \), so we have \( b^3 \).
- For \( c \): The lowest power is \( \min(4, 3) = 3 \), so we have \( c^3 \).

Thus, the HCF is:
\[ \text{HCF} = a^2b^3c^3 \]

### Step 3: Calculate the LCM
The LCM is found by taking the highest power of each variable from both expressions.

- For \( a \): The highest power is \( \max(2, 5) = 5 \), so we have \( a^5 \).
- For \( b \): The highest power is \( \max(3, 4) = 4 \), so we have \( b^4 \).
- For \( c \): The highest power is \( \max(4, 3) = 4 \), so we have \( c^4 \).

Thus, the LCM is:
\[ \text{LCM} = a^5b^4c^4 \]

### Final Answer:
- HCF: \( a^2b^3c^3 \)
- LCM: \( a^5b^4c^4 \)

---