What is the least possible no. which must be added to 4722, so that it becomes divisible by 21, 25, 27 and 35 ?

Answer

To find the least possible number that must be added to 4722 so that it becomes divisible by 21, 25, 27, and 35, we can follow these steps:

### Step 1: Find the LCM of the numbers
First, we need to find the least common multiple (LCM) of the numbers 21, 25, 27, and 35.

- **Prime Factorization:**
- 21 = 3 × 7
- 25 = 5²
- 27 = 3³
- 35 = 5 × 7

- **Identify the highest powers of all prime factors:**
- The highest power of 3 is 3³ (from 27).
- The highest power of 5 is 5² (from 25).
- The highest power of 7 is 7¹ (from 21 and 35).

- **Calculate the LCM:**
\[ \text{LCM} = 3^3 \times 5^2 \times 7^1 = 27 \times 25 \times 7 \]

Calculating this step by step:
1. \( 27 \times 25 = 675 \)
2. \( 675 \times 7 = 4725 \)

Thus, the LCM of 21, 25, 27, and 35 is **4725**.

### Step 2: Determine how much to add to 4722
Next, we need to find out how much we need to add to 4722 to make it divisible by 4725.

- **Calculate the difference:**
\[ 4725 - 4722 = 3 \]

### Conclusion
The least possible number that must be added to 4722 to make it divisible by 21, 25, 27, and 35 is **3**.

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