Find the smallest number which is divisible by 18,15 and 12

Options

A. `140`
B. `160`
C. `180`
D. `190`

Explanation

To find the smallest number which is divisible by 18, 15, and 12, we need to calculate the Least Common Multiple (LCM) of these three numbers. Here’s a step-by-step solution:

### Step 1: Prime Factorization
First, we need to find the prime factorization of each number.

- **18**:
- 18 = 2 × 3²
- **15**:
- 15 = 3 × 5
- **12**:
- 12 = 2² × 3

### Step 2: Identify the Highest Powers of Each Prime Factor
Next, we identify the highest power of each prime factor from the factorizations:

- For **2**: The highest power is 2² (from 12).
- For **3**: The highest power is 3² (from 18).
- For **5**: The highest power is 5¹ (from 15).

### Step 3: Multiply the Highest Powers Together
Now we multiply these highest powers together to find the LCM:

LCM = 2² × 3² × 5¹

Calculating this step-by-step:

1. Calculate 2²:
- 2² = 4
2. Calculate 3²:
- 3² = 9
3. Multiply 4 and 9:
- 4 × 9 = 36
4. Finally, multiply 36 by 5:
- 36 × 5 = 180

### Conclusion
Thus, the smallest number which is divisible by 18, 15, and 12 is **180**.

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