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find the smallest number which when divided by 35,50,80 leaves reminder 9 in each case
? Related: Chapter Notes - Playing with Numbers
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find the smallest number which when divided by 35,50,80 leaves remind...
Solution:
To find the smallest number which when divided by 35, 50, and 80 leaves a reminder of 9 in each case, we need to use the concept of LCM (Least Common Multiple) and then add 9 to it.
Step 1: Finding the LCM of 35, 50, and 80
Prime factorizing the given numbers, we get:
35 = 5 x 7
50 = 2 x 5 x 5
80 = 2 x 2 x 2 x 2 x 5
The LCM of 35, 50, and 80 is the product of the highest powers of all the prime factors present in the given numbers. Therefore, LCM(35, 50, 80) = 2^4 x 5^2 x 7 = 2800.
Step 2: Adding 9 to the LCM
Now, we need to add 9 to the LCM to get the smallest number which when divided by 35, 50, and 80 leaves a reminder of 9 in each case.
Smallest number = LCM(35, 50, 80) + 9 = 2800 + 9 = 2809
Therefore, the smallest number which when divided by 35, 50, and 80 leaves a reminder of 9 in each case is 2809.
Conclusion:
- To find the smallest number which when divided by given numbers leaves a reminder, we need to find the LCM of the given numbers.
- After finding the LCM, we need to add the given reminder to it to get the smallest number which satisfies the given conditions.
- In this case, the smallest number is 2809.
To find the smallest number which when divided by 35, 50, and 80 leaves a reminder of 9 in each case, we need to use the concept of LCM (Least Common Multiple) and then add 9 to it.
Step 1: Finding the LCM of 35, 50, and 80
Prime factorizing the given numbers, we get:
35 = 5 x 7
50 = 2 x 5 x 5
80 = 2 x 2 x 2 x 2 x 5
The LCM of 35, 50, and 80 is the product of the highest powers of all the prime factors present in the given numbers. Therefore, LCM(35, 50, 80) = 2^4 x 5^2 x 7 = 2800.
Step 2: Adding 9 to the LCM
Now, we need to add 9 to the LCM to get the smallest number which when divided by 35, 50, and 80 leaves a reminder of 9 in each case.
Smallest number = LCM(35, 50, 80) + 9 = 2800 + 9 = 2809
Therefore, the smallest number which when divided by 35, 50, and 80 leaves a reminder of 9 in each case is 2809.
Conclusion:
- To find the smallest number which when divided by given numbers leaves a reminder, we need to find the LCM of the given numbers.
- After finding the LCM, we need to add the given reminder to it to get the smallest number which satisfies the given conditions.
- In this case, the smallest number is 2809.
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find the smallest number which when divided by 35,50,80 leaves reminder 9 in each case Related: Chapter Notes - Playing with Numbers?
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find the smallest number which when divided by 35,50,80 leaves reminder 9 in each case Related: Chapter Notes - Playing with Numbers? 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 smallest number which when divided by 35,50,80 leaves reminder 9 in each case Related: Chapter Notes - Playing with Numbers? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find the smallest number which when divided by 35,50,80 leaves reminder 9 in each case Related: Chapter Notes - Playing with Numbers?.
find the smallest number which when divided by 35,50,80 leaves reminder 9 in each case Related: Chapter Notes - Playing with Numbers? 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 smallest number which when divided by 35,50,80 leaves reminder 9 in each case Related: Chapter Notes - Playing with Numbers? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find the smallest number which when divided by 35,50,80 leaves reminder 9 in each case Related: Chapter Notes - Playing with Numbers?.
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