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Find the least number which when divided by 16 ,34 and 40 leaves 5 as remainder in each case. Solve it according to a class 6 girl.?
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Find the least number which when divided by 16 ,34 and 40 leaves 5 as ...
To find the least number that, when divided by 16, 34, and 40, leaves a remainder of 5, we can follow these steps:
Understanding the Problem
- We need to find a number \( x \) such that:
- \( x \mod 16 = 5 \)
- \( x \mod 34 = 5 \)
- \( x \mod 40 = 5 \)
Adjusting the Condition
- Since \( x \) leaves a remainder of 5, we can express \( x \) as:
- \( x = 16k + 5 \)
- \( x = 34m + 5 \)
- \( x = 40n + 5 \)
Here, \( k, m, n \) are integers.
- To simplify, we can subtract 5 from all sides:
- \( x - 5 = 16k \)
- \( x - 5 = 34m \)
- \( x - 5 = 40n \)
- This means \( x - 5 \) must be a common multiple of 16, 34, and 40.
Finding the Least Common Multiple (LCM)
- First, we need to calculate the LCM of 16, 34, and 40.
- Prime Factorization:
- 16 = \( 2^4 \)
- 34 = \( 2^1 \times 17^1 \)
- 40 = \( 2^3 \times 5^1 \)
- Taking the highest powers:
- LCM = \( 2^4 \times 5^1 \times 17^1 = 16 \times 5 \times 17 \)
Calculating the LCM
- First, calculate \( 16 \times 5 = 80 \).
- Now calculate \( 80 \times 17 = 1360 \).
Final Calculation
- Since \( x - 5 = 1360 \), we find \( x \):
- \( x = 1360 + 5 = 1365 \).
Conclusion
- The least number which, when divided by 16, 34, and 40, leaves a remainder of 5 is 1365.
Understanding the Problem
- We need to find a number \( x \) such that:
- \( x \mod 16 = 5 \)
- \( x \mod 34 = 5 \)
- \( x \mod 40 = 5 \)
Adjusting the Condition
- Since \( x \) leaves a remainder of 5, we can express \( x \) as:
- \( x = 16k + 5 \)
- \( x = 34m + 5 \)
- \( x = 40n + 5 \)
Here, \( k, m, n \) are integers.
- To simplify, we can subtract 5 from all sides:
- \( x - 5 = 16k \)
- \( x - 5 = 34m \)
- \( x - 5 = 40n \)
- This means \( x - 5 \) must be a common multiple of 16, 34, and 40.
Finding the Least Common Multiple (LCM)
- First, we need to calculate the LCM of 16, 34, and 40.
- Prime Factorization:
- 16 = \( 2^4 \)
- 34 = \( 2^1 \times 17^1 \)
- 40 = \( 2^3 \times 5^1 \)
- Taking the highest powers:
- LCM = \( 2^4 \times 5^1 \times 17^1 = 16 \times 5 \times 17 \)
Calculating the LCM
- First, calculate \( 16 \times 5 = 80 \).
- Now calculate \( 80 \times 17 = 1360 \).
Final Calculation
- Since \( x - 5 = 1360 \), we find \( x \):
- \( x = 1360 + 5 = 1365 \).
Conclusion
- The least number which, when divided by 16, 34, and 40, leaves a remainder of 5 is 1365.
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Find the least number which when divided by 16 ,34 and 40 leaves 5 as remainder in each case. Solve it according to a class 6 girl.?
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Find the least number which when divided by 16 ,34 and 40 leaves 5 as remainder in each case. Solve it according to a class 6 girl.? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Find the least number which when divided by 16 ,34 and 40 leaves 5 as remainder in each case. Solve it according to a class 6 girl.? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the least number which when divided by 16 ,34 and 40 leaves 5 as remainder in each case. Solve it according to a class 6 girl.?.
Find the least number which when divided by 16 ,34 and 40 leaves 5 as remainder in each case. Solve it according to a class 6 girl.? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Find the least number which when divided by 16 ,34 and 40 leaves 5 as remainder in each case. Solve it according to a class 6 girl.? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the least number which when divided by 16 ,34 and 40 leaves 5 as remainder in each case. Solve it according to a class 6 girl.?.
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