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Find three digit largest number that will exactly divides 2,8, 12?
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Find three digit largest number that will exactly divides 2,8, 12?
Understanding the Problem
To find the largest three-digit number that exactly divides 2, 8, and 12, we first need to determine the Least Common Multiple (LCM) of these numbers. The LCM is the smallest number that is a multiple of all given numbers.
Finding the LCM
1. Prime Factorization:
- 2 = 2
- 8 = 2^3
- 12 = 2^2 × 3
2. Take the Highest Power of Each Prime:
- The highest power of 2 is 2^3 (from 8).
- The highest power of 3 is 3^1 (from 12).
3. Calculate the LCM:
- LCM = 2^3 × 3^1 = 8 × 3 = 24
Finding the Largest Three-Digit Number
To find the largest three-digit number that is a multiple of 24, we need to divide 999 (the largest three-digit number) by 24 and round down to the nearest whole number.
1. Division:
- 999 ÷ 24 = 41.625
2. Rounding Down:
- The largest whole number is 41.
3. Multiplying Back:
- 41 × 24 = 984
Conclusion
The largest three-digit number that exactly divides 2, 8, and 12 is 984. This number is a multiple of the LCM we calculated, ensuring it meets the criteria of being divisible by all three original numbers.
To find the largest three-digit number that exactly divides 2, 8, and 12, we first need to determine the Least Common Multiple (LCM) of these numbers. The LCM is the smallest number that is a multiple of all given numbers.
Finding the LCM
1. Prime Factorization:
- 2 = 2
- 8 = 2^3
- 12 = 2^2 × 3
2. Take the Highest Power of Each Prime:
- The highest power of 2 is 2^3 (from 8).
- The highest power of 3 is 3^1 (from 12).
3. Calculate the LCM:
- LCM = 2^3 × 3^1 = 8 × 3 = 24
Finding the Largest Three-Digit Number
To find the largest three-digit number that is a multiple of 24, we need to divide 999 (the largest three-digit number) by 24 and round down to the nearest whole number.
1. Division:
- 999 ÷ 24 = 41.625
2. Rounding Down:
- The largest whole number is 41.
3. Multiplying Back:
- 41 × 24 = 984
Conclusion
The largest three-digit number that exactly divides 2, 8, and 12 is 984. This number is a multiple of the LCM we calculated, ensuring it meets the criteria of being divisible by all three original numbers.
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Find three digit largest number that will exactly divides 2,8, 12? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Find three digit largest number that will exactly divides 2,8, 12? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find three digit largest number that will exactly divides 2,8, 12?.
Find three digit largest number that will exactly divides 2,8, 12? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Find three digit largest number that will exactly divides 2,8, 12? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find three digit largest number that will exactly divides 2,8, 12?.
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