LCM Calculation for Divisibility
To find the least number to add to 3496 for divisibility by 2, 6, 4, and 3, we first need the Least Common Multiple (LCM) of these numbers.
- Prime factorization: $2 = 2$; $6 = 2 \times 3$; $4 = 2^2$; $3 = 3$.
- LCM is $2^2 \times 3 = 12$.
The LCM of 2, 6, 4, and 3 is 12.
Division and Remainder Calculation
Now, divide the given number 3496 by the LCM (12) to find the remainder.
$ 3496 \div 12 $
Performing the division:
- $3496 = 12 \times 291 + 4$.
The remainder is 4.
Finding the Least Number to Add
The least number to add is the difference needed to reach the next multiple of the LCM (12).
Number to add = $LCM - Remainder$
Number to add = $12 - 4 = 8$.
Adding 8 to 3496 results in $3496 + 8 = 3504$.
Verification: $3504 \div 12 = 292$. This confirms 3504 is exactly divisible by 12.
Thus, the least number required is 8.
Similar Questions
- The smallest positive number which must be added to the greatest number of 4 digits in order that the sum may be exactly divisible by 307 is:
- What is the remainder when $7^{29} + 4$ is divided by 6?
- How many numbers are there between 1000 and 3000 that are completely divisible by 7?
- What least number should be added to 3500 to make it exactly divisible by 42, 49, 56 and 63?
- Find the remainder when $7^6 + 5$ is divided by 6.
- On dividing 15,971 by a certain number, the quotient is 55 and the remainder is 21. Find the divisor.
- A maximum of how many pieces of exact 17 cm length can be cut from a 960 cm long rod?
- A number when divided by 7 leaves a remainder 4. What will be the remainder when the square of the same number is divided by 7?
The remainder in the expression $27\frac{3}{4}$ is:
- Find the smallest 4-digit number which when divided by 2, 3 and 5 leaves a remainder of 1 in each case?
Important Questions from Divisibility and Remainder
If a five digit number 247xy is divisible by 3, 7 and 11, then what is the value of (2y - 8x)?
If the seven-digit number 94x29y6 is divisible by 72, then what is the value of (2x + 3y) for x ≠ y ?
Find the greatest value of b so that 30a68b (a > b) is divisible by 11.
What is the remainder when the product of 335, 608 and 853 is divided by 13?
- What is the least square number which is exactly divisible by 2, 3, 10, 18 and 20?
