Find the least natural number which when divided by 6,9, 12 and 18 leaves no remainders.

Options

A. 36
B. 72
C. 12
D. 18

Answer

To find the least natural number that leaves no remainder when divided by 6, 9, 12, and 18, we need to calculate the Least Common Multiple (LCM) of these numbers. Here's how we can do it step by step:

### Step 1: List the Numbers
We start with the numbers given in the question:
- 6
- 9
- 12
- 18

### Step 2: Prime Factorization
Next, we find the prime factorization of each number:
- **6** = 2 × 3
- **9** = 3 × 3 = 3²
- **12** = 2² × 3
- **18** = 2 × 3²

### Step 3: Identify the Highest Powers of Each Prime
Now, we identify the highest power of each prime number that appears in the factorizations:
- For **2**, the highest power is 2² (from 12).
- For **3**, the highest power is 3² (from 9 and 18).

### Step 4: Calculate the LCM
To find the LCM, we multiply these highest powers together:
- LCM = 2² × 3²
- LCM = 4 × 9
- LCM = 36

### Conclusion
The least natural number which when divided by 6, 9, 12, and 18 leaves no remainder is **36**.

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