Find the least number which when divided by 24, 36 and 48 leaves zero as its remainder.

Options

A. 124
B. 144
C. 164
D. 224

Answer

To find the least number which, when divided by 24, 36, and 48, leaves zero as its remainder, we need to determine the Least Common Multiple (LCM) of these three numbers. Here’s how to solve it step by step:

### Step 1: Find the prime factorization of each number.
- **24**:
- 24 = 2 × 12
- 12 = 2 × 6
- 6 = 2 × 3
- Therefore, 24 = 2^3 × 3^1

- **36**:
- 36 = 2 × 18
- 18 = 2 × 9
- 9 = 3 × 3
- Therefore, 36 = 2^2 × 3^2

- **48**:
- 48 = 2 × 24
- 24 = 2 × 12
- 12 = 2 × 6
- 6 = 2 × 3
- Therefore, 48 = 2^4 × 3^1

### Step 2: Identify the highest power of each prime factor.
- For the prime factor **2**:
- The highest power is 2^4 (from 48).

- For the prime factor **3**:
- The highest power is 3^2 (from 36).

### Step 3: Calculate the LCM using the highest powers.
- LCM = 2^4 × 3^2

### Step 4: Calculate the numerical value of the LCM.
- 2^4 = 16
- 3^2 = 9
- Now, multiply these together:
- LCM = 16 × 9 = 144

### Conclusion:
The least number which, when divided by 24, 36, and 48, leaves zero as its remainder is **144**.

---