Which among the following numbers is exactely divsible by 11,13 and 7 ?
(a)62613
(b) 62424
(c) 624635
(d) 424646

Options

A. (a)
B. (c)
C. (d)
D. (b)

Answer

To determine which of the given numbers is exactly divisible by 11, 13, and 7, we will follow these steps:

### Step 1: Calculate the LCM of 11, 13, and 7
- Since 11, 13, and 7 are all prime numbers, their least common multiple (LCM) is simply their product.
- LCM = 7 × 11 × 13

### Step 2: Perform the multiplication
- First, calculate 7 × 11 = 77.
- Then, multiply 77 by 13:
- 77 × 13 = 1001.

### Step 3: Check divisibility of each option by 1001
- We need to check which of the given options is divisible by 1001.
- The options are:
- (a) 62613
- (b) 62424
- (c) 624635
- (d) 424646

### Step 4: Perform the division for each option
1. **For option (a) 62613**:
- 62613 ÷ 1001 = 62.59 (not divisible)

2. **For option (b) 62424**:
- 62424 ÷ 1001 = 62.00 (divisible)

3. **For option (c) 624635**:
- 624635 ÷ 1001 = 624.01 (not divisible)

4. **For option (d) 424646**:
- 424646 ÷ 1001 = 424.22 (not divisible)

### Step 5: Conclusion
- The only number that is exactly divisible by 11, 13, and 7 is **62424**.

### Final Answer:
(b) 62424