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Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.?
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Find the least number which when divided by 6, 15 and 18 leave remaind...
Solution:
Finding the least number:
- Let the least number be x.
- According to the given conditions,
- x = 6a + 5 (where a is an integer)
- x = 15b + 5 (where b is an integer)
- x = 18c + 5 (where c is an integer)
Finding the common multiple of 6, 15, and 18:
- Find the LCM of 6, 15, and 18.
- LCM(6, 15, 18) = 90
Finding the least number:
- Substitute x = 90k + 5 in the above equations, where k is an integer.
- 90k + 5 = 6a + 5
- 90k + 5 = 15b + 5
- 90k + 5 = 18c + 5
- Simplify the equations to find the values of a, b, and c.
Putting the values back:
- Substitute the values of a, b, and c back into x = 90k + 5 to find the least number that satisfies all the given conditions.
Conclusion:
- The least number that when divided by 6, 15, and 18 leaves a remainder of 5 in each case is the number obtained by substituting the values of a, b, and c into x = 90k + 5.
Finding the least number:
- Let the least number be x.
- According to the given conditions,
- x = 6a + 5 (where a is an integer)
- x = 15b + 5 (where b is an integer)
- x = 18c + 5 (where c is an integer)
Finding the common multiple of 6, 15, and 18:
- Find the LCM of 6, 15, and 18.
- LCM(6, 15, 18) = 90
Finding the least number:
- Substitute x = 90k + 5 in the above equations, where k is an integer.
- 90k + 5 = 6a + 5
- 90k + 5 = 15b + 5
- 90k + 5 = 18c + 5
- Simplify the equations to find the values of a, b, and c.
Putting the values back:
- Substitute the values of a, b, and c back into x = 90k + 5 to find the least number that satisfies all the given conditions.
Conclusion:
- The least number that when divided by 6, 15, and 18 leaves a remainder of 5 in each case is the number obtained by substituting the values of a, b, and c into x = 90k + 5.
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Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.?
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Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.? 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 6, 15 and 18 leave remainder 5 in each case.? 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 6, 15 and 18 leave remainder 5 in each case.?.
Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.? 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 6, 15 and 18 leave remainder 5 in each case.? 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 6, 15 and 18 leave remainder 5 in each case.?.
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