The Lowest No. Which Leaves 6 As A Reminder When Divided By 10,20,nd 40 Is Called As?
The Lowest Number Which Leaves 6 as a Remainder When Divided by 10, 20, and 40
In mathematics, finding the lowest number that satisfies a certain condition is a common problem. In this article, we will explore the concept of finding the lowest number that leaves 6 as a remainder when divided by 10, 20, and 40. This problem is a classic example of a mathematical puzzle that requires careful analysis and understanding of the underlying concepts.
To solve this problem, we need to understand the concept of remainders and divisibility. When a number is divided by another number, the remainder is the amount left over after the division. For example, if we divide 17 by 5, the quotient is 3 and the remainder is 2. In this case, the remainder is 2 because 17 is 2 more than a multiple of 5.
Finding the Least Common Multiple (LCM)
The first step in solving this problem is to find the least common multiple (LCM) of 10, 20, and 40. The LCM is the smallest number that is a multiple of all the given numbers. In this case, the LCM of 10, 20, and 40 is 40.
Using the LCM to Find the Solution
Now that we have found the LCM, we can use it to find the solution to the problem. We know that the number we are looking for leaves 6 as a remainder when divided by 10, 20, and 40. This means that the number is 6 more than a multiple of the LCM.
Calculating the Solution
To calculate the solution, we can add 6 to the LCM. This gives us:
40 + 6 = 46
Therefore, the lowest number that leaves 6 as a remainder when divided by 10, 20, and 40 is 46.
Verifying the Solution
To verify the solution, we can divide 46 by 10, 20, and 40 and check if the remainder is indeed 6.
- 46 ÷ 10 = 4 with a remainder of 6
- 46 ÷ 20 = 2 with a remainder of 6
- 46 ÷ 40 = 1 with a remainder of 6
As we can see, the remainder is indeed 6 in all cases, which confirms that our solution is correct.
In conclusion, the lowest number that leaves 6 as a remainder when divided by 10, 20, and 40 is 46. This problem requires a good understanding of the concept of remainders and divisibility, as well as the ability to find the least common multiple (LCM) of a set of numbers. By following the steps outlined in this article, we can solve this problem and find the solution.
- Q: What is the least common multiple (LCM) of 10, 20, and 40? A: The LCM of 10, 20, and 40 is 40.
- Q: How do I find the solution to this problem? A: To find the solution, add 6 to the LCM.
- Q: How do I verify the solution? A: Divide the solution by 10, 20, and 40 and check if the remainder is indeed 6.
- Remainders and divisibility
- Least common multiple (LCM)
- Mathematical puzzles and problems
A: The LCM of 10, 20, and 40 is 40.
A: To find the solution, add 6 to the LCM. In this case, the solution is 40 + 6 = 46.
A: To verify the solution, divide the solution by 10, 20, and 40 and check if the remainder is indeed 6.
- 46 ÷ 10 = 4 with a remainder of 6
- 46 ÷ 20 = 2 with a remainder of 6
- 46 ÷ 40 = 1 with a remainder of 6
A: To find the solution for a different set of numbers, you need to find the LCM of those numbers and then add 6 to it.
A: Yes, you can use a calculator to find the solution. However, it's always a good idea to understand the underlying math and verify the solution manually.
A: If you get a different solution using a calculator, it's possible that the calculator is incorrect or that you made a mistake in entering the numbers. Double-check your work and verify the solution manually.
A: Yes, this method can be used to find the solution for other types of problems that involve finding the LCM and adding a remainder.
A: Some common mistakes to avoid when solving this type of problem include:
- Not finding the LCM correctly
- Not adding the remainder correctly
- Not verifying the solution manually
- Using a calculator incorrectly
A: You can practice solving this type of problem by:
- Working through examples and exercises
- Using online resources and calculators
- Asking a teacher or tutor for help
- Joining a study group or math club
A: Some real-world applications of this type of problem include:
- Finding the least common multiple of a set of numbers in finance and accounting
- Determining the smallest unit of measurement in science and engineering
- Finding the solution to a system of linear equations in mathematics and computer science
A: Yes, this method can be used to solve other types of problems that involve remainders. However, you may need to modify the method to suit the specific problem.
A: Some common types of problems that involve remainders include:
- Finding the remainder when a number is divided by another number
- Finding the smallest number that leaves a certain remainder when divided by a set of numbers
- Finding the largest number that leaves a certain remainder when divided by a set of numbers
A: You can learn more about remainders and divisibility by:
- Reading online resources and textbooks
- Watching video tutorials and lectures
- Practicing problems and exercises
- Asking a teacher or tutor for help