Find the least numbers which should be added to 3857 so that the sum is exactly divisible by 5, 6, 4 and 3

Options

A. 43
B. 3
C. 33
D. 17

Answer

To find the least number that should be added to 3857 so that the sum is exactly divisible by 5, 6, 4, and 3, we will follow these steps:

### Step 1: Find the LCM of 5, 6, 4, and 3
To find the least common multiple (LCM), we first find the prime factorization of each number:
- 5 = 5
- 6 = 2 × 3
- 4 = 2²
- 3 = 3

Now, we take the highest power of each prime factor:
- The highest power of 2 is 2² (from 4)
- The highest power of 3 is 3¹ (from 6 and 3)
- The highest power of 5 is 5¹ (from 5)

Thus, the LCM is:
\[ LCM = 2² × 3¹ × 5¹ = 4 × 3 × 5 = 60 \]

### Step 2: Find the nearest multiple of LCM (60) greater than 3857
Next, we need to find the smallest multiple of 60 that is greater than 3857. We divide 3857 by 60:
\[ 3857 ÷ 60 \approx 64.2833 \]
The next whole number is 65, so we multiply:
\[ 60 × 65 = 3900 \]

### Step 3: Calculate the difference between 3900 and 3857
Now, we find the difference between 3900 and 3857:
\[ 3900 - 3857 = 43 \]

### Conclusion
The least number that should be added to 3857 to make it divisible by 5, 6, 4, and 3 is **43**.

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