(Smallest common multiple of 36 and 60) / (Biggest common factor of 18 and 45) is equal to

Options

A. 20
B. 30
C. 40
D. 10

Answer

To solve the problem, we will follow these steps:

### Step 1: Find the Smallest Common Multiple (LCM) of 36 and 60.

1. **Prime Factorization of 36**:
- 36 = 2 × 2 × 3 × 3 = \(2^2 \times 3^2\)

2. **Prime Factorization of 60**:
- 60 = 2 × 2 × 3 × 5 = \(2^2 \times 3^1 \times 5^1\)

3. **Determine the LCM**:
- Take the highest power of each prime factor:
- For 2: \(2^2\)
- For 3: \(3^2\)
- For 5: \(5^1\)
- Therefore, LCM = \(2^2 \times 3^2 \times 5^1\)

4. **Calculate the LCM**:
- LCM = \(4 \times 9 \times 5 = 180\)

### Step 2: Find the Biggest Common Factor (GCF) of 18 and 45.

1. **Prime Factorization of 18**:
- 18 = 2 × 3 × 3 = \(2^1 \times 3^2\)

2. **Prime Factorization of 45**:
- 45 = 3 × 3 × 5 = \(3^2 \times 5^1\)

3. **Determine the GCF**:
- Take the lowest power of each common prime factor:
- For 3: \(3^2\)
- Therefore, GCF = \(3^2 = 9\)

### Step 3: Divide the LCM by the GCF.

1. **Perform the Division**:
- \(\frac{LCM}{GCF} = \frac{180}{9} = 20\)

### Final Answer:
The result of the expression \((\text{Smallest common multiple of } 36 \text{ and } 60) / (\text{Biggest common factor of } 18 \text{ and } 45)\) is **20**.

---