(Smallest common multiple of 36, 60 and 72) / (Biggest common factor of 18, 45 and 36) is equal to

Options

A. 20
B. 30
C. 40
D. 50

Answer

To solve the problem, we need to find the smallest common multiple (LCM) of 36, 60, and 72, and then divide that by the biggest common factor (HCF) of 18, 45, and 36.

### Step 1: Find the LCM of 36, 60, and 72

1. **Prime Factorization**:
- 36 = 2² × 3²
- 60 = 2¹ × 3¹ × 5¹
- 72 = 2³ × 3²

2. **Identify the highest power of each prime factor**:
- For 2: highest power is 2³ (from 72)
- For 3: highest power is 3² (from both 36 and 72)
- For 5: highest power is 5¹ (from 60)

3. **Calculate the LCM**:
\[ \text{LCM} = 2^3 × 3^2 × 5^1 = 8 × 9 × 5 \]
\[ = 72 × 5 = 360 \]

### Step 2: Find the HCF of 18, 45, and 36

1. **Prime Factorization**:
- 18 = 2¹ × 3²
- 45 = 3² × 5¹
- 36 = 2² × 3²

2. **Identify the lowest power of each common prime factor**:
- For 2: lowest power is 2¹ (from 18)
- For 3: lowest power is 3² (common in all)
- 5 is not common in all three.

3. **Calculate the HCF**:
\[ \text{HCF} = 3^2 = 9 \]

### Step 3: Divide the LCM by the HCF

Now we divide the LCM by the HCF:
\[ \frac{\text{LCM}}{\text{HCF}} = \frac{360}{9} = 40 \]

### Final Answer:
The result of the operation is **40**.

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