Find the G.C.F . & L.C.M. of 20 and 28.
A. 20,280
B. 5,280
C. 10,140
D. 4,140

Options

A. B
B. D
C. C
D. A

Answer

To find the G.C.F. (Greatest Common Factor) and L.C.M. (Lowest Common Multiple) of 20 and 28, we will follow these steps:

### Step 1: Find the Factors of Each Number
- **Factors of 20**:
- The factors of 20 are: 1, 2, 4, 5, 10, 20.

- **Factors of 28**:
- The factors of 28 are: 1, 2, 4, 7, 14, 28.

### Step 2: Identify the Common Factors
- The common factors of 20 and 28 are: 1, 2, 4.

### Step 3: Determine the Greatest Common Factor (G.C.F.)
- Among the common factors (1, 2, 4), the greatest one is **4**.
- Therefore, G.C.F. of 20 and 28 is **4**.

### Step 4: Find the Multiples of Each Number
- **Multiples of 20**:
- The multiples of 20 are: 20, 40, 60, 80, 100, 120, 140, ...

- **Multiples of 28**:
- The multiples of 28 are: 28, 56, 84, 112, 140, ...

### Step 5: Identify the Common Multiples
- The common multiples of 20 and 28 are: 140, ...

### Step 6: Determine the Lowest Common Multiple (L.C.M.)
- The smallest common multiple is **140**.
- Therefore, L.C.M. of 20 and 28 is **140**.

### Final Answer
- G.C.F. = 4
- L.C.M. = 140

Thus, the answer is **4 and 140**, which corresponds to option D.

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