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

Options

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

Answer

To solve the problem of finding the sum of the HCF (Highest Common Factor) and LCM (Least Common Multiple) of the numbers 4, 20, and 28, we can follow these steps:

### Step 1: Find the HCF of 4, 20, and 28
To find the HCF, we can list the factors of each number:

- Factors of 4: 1, 2, 4
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 28: 1, 2, 4, 7, 14, 28

Now, identify the common factors:
- Common factors: 1, 2, 4

The highest common factor is **4**.

### Step 2: Find the LCM of 4, 20, and 28
To find the LCM, we can use the prime factorization method:

- Prime factorization of 4: \(2^2\)
- Prime factorization of 20: \(2^2 \times 5^1\)
- Prime factorization of 28: \(2^2 \times 7^1\)

Now, take the highest power of each prime number from the factorizations:
- For \(2\): highest power is \(2^2\)
- For \(5\): highest power is \(5^1\)
- For \(7\): highest power is \(7^1\)

Now, multiply these together to find the LCM:
\[ LCM = 2^2 \times 5^1 \times 7^1 = 4 \times 5 \times 7 = 140 \]

### Step 3: Sum of HCF and LCM
Now, we can find the sum of the HCF and LCM:
\[ \text{Sum} = HCF + LCM = 4 + 140 = 144 \]

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

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