Sum of HCF and LCM of 4,20 and 28 is

Options

A. 140
B. 144
C. 74
D. 136

Answer

To find the sum of the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of the numbers 4, 20, and 28, we will follow these steps:

### Step 1: Find the Prime Factorization of Each Number
- **4**: The prime factorization of 4 is \(2^2\).
- **20**: The prime factorization of 20 is \(2^2 \times 5\).
- **28**: The prime factorization of 28 is \(2^2 \times 7\).

### Step 2: Determine the HCF
The HCF is found by taking the lowest power of all prime factors present in each of the numbers.
- The common prime factor is **2**.
- The lowest power of 2 in the factorizations is \(2^2\).
- Therefore, the HCF of 4, 20, and 28 is \(2^2 = 4\).

### Step 3: Determine the LCM
The LCM is found by taking the highest power of all prime factors present in any of the numbers.
- For the prime factor **2**, the highest power is \(2^2\).
- For the prime factor **5**, the highest power is \(5^1\).
- For the prime factor **7**, the highest power is \(7^1\).
- Therefore, the LCM is calculated as:
\[ LCM = 2^2 \times 5^1 \times 7^1 = 4 \times 5 \times 7 \]
Calculating this step-by-step:
- \(4 \times 5 = 20\)
- \(20 \times 7 = 140\)
So, the LCM of 4, 20, and 28 is 140.

### Step 4: Calculate the Sum of HCF and LCM
Now, we will find the sum of the HCF and LCM:
\[ \text{Sum} = \text{HCF} + \text{LCM} = 4 + 140 = 144 \]

### Final Answer
The sum of the HCF and LCM of 4, 20, and 28 is **144**.

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