Find the least number which should be added to 2430 so that the sum is exactly divisible by 5, 4 and 2

Options

A. a. 3
B. b. 10
C. c. 13
D. d. 33

Answer

To find the least number that should be added to 2430 so that the sum is exactly divisible by 5, 4, and 2, we can follow these steps:

### Step 1: Find the LCM of 5, 4, and 2
To ensure that the sum is divisible by all three numbers, we first need to find the Least Common Multiple (LCM) of these numbers.

- The prime factorization of 5 is \(5^1\).
- The prime factorization of 4 is \(2^2\).
- The prime factorization of 2 is \(2^1\).

Now, we take the highest power of each prime:
- For 2, the highest power is \(2^2\).
- For 5, the highest power is \(5^1\).

Thus, the LCM is:
\[ LCM = 2^2 \times 5^1 = 4 \times 5 = 20 \]

### Step 2: Divide 2430 by the LCM (20) and find the remainder
Next, we divide 2430 by 20 to find the remainder.

\[ 2430 \div 20 = 121.5 \quad \text{(we only need the integer part)} \]
Calculating the product:
\[ 20 \times 121 = 2420 \]
Now, we find the remainder:
\[ 2430 - 2420 = 10 \]

### Step 3: Calculate the number to be added
To make 2430 divisible by 20, we need to subtract the remainder from the LCM (20):
\[ 20 - 10 = 10 \]

### Conclusion
Thus, the least number that should be added to 2430 to make it divisible by 5, 4, and 2 is:
\[ \boxed{10} \]

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