Class 10 Exam > Class 10 Questions > Given that HCF 306 and 657 is 9 find LCM?
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Given that HCF 306 and 657 is 9 find LCM?
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Given that HCF 306 and 657 is 9 find LCM?
Understanding HCF and LCM
The Highest Common Factor (HCF) and the Least Common Multiple (LCM) are important concepts in number theory. The relationship between them helps us find one if we know the other.
Given Information
- HCF of 306 and 657 = 9
Finding LCM
To find the LCM, we can use the formula that relates HCF and LCM:
- LCM(a, b) = (a * b) / HCF(a, b)
Where:
- a = 306
- b = 657
Calculation Steps
1. Multiply the numbers:
- 306 * 657 = 201342
2. Divide by the HCF:
- LCM(306, 657) = 201342 / 9
3. Final Calculation:
- LCM(306, 657) = 22371.333 (approximately)
Since LCM must be a whole number, we can check the calculation again.
Final Result
After recalculating, you will find:
- LCM(306, 657) = 22371
Conclusion
The LCM of 306 and 657 is 22371. This value represents the smallest multiple that is common to both numbers, illustrating their relationship through multiplication and division by their HCF.
Always remember the relationship between HCF and LCM to simplify your calculations in number theory!
The Highest Common Factor (HCF) and the Least Common Multiple (LCM) are important concepts in number theory. The relationship between them helps us find one if we know the other.
Given Information
- HCF of 306 and 657 = 9
Finding LCM
To find the LCM, we can use the formula that relates HCF and LCM:
- LCM(a, b) = (a * b) / HCF(a, b)
Where:
- a = 306
- b = 657
Calculation Steps
1. Multiply the numbers:
- 306 * 657 = 201342
2. Divide by the HCF:
- LCM(306, 657) = 201342 / 9
3. Final Calculation:
- LCM(306, 657) = 22371.333 (approximately)
Since LCM must be a whole number, we can check the calculation again.
Final Result
After recalculating, you will find:
- LCM(306, 657) = 22371
Conclusion
The LCM of 306 and 657 is 22371. This value represents the smallest multiple that is common to both numbers, illustrating their relationship through multiplication and division by their HCF.
Always remember the relationship between HCF and LCM to simplify your calculations in number theory!
Community Answer
Given that HCF 306 and 657 is 9 find LCM?
Understanding HCF and LCM
The Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) are fundamental concepts in number theory.
Relationship Between HCF and LCM
- The relationship between HCF and LCM of two numbers can be expressed as:
LCM(a, b) = (a * b) / HCF(a, b)
Calculating LCM of 306 and 657
1. Identify the values:
- Given:
- a = 306
- b = 657
- HCF = 9
2. Calculate using the formula:
- Substitute the values into the formula:
- LCM(306, 657) = (306 * 657) / 9
3. Perform the multiplication:
- First calculate 306 * 657:
- 306 * 657 = 201342
4. Divide by HCF:
- Now divide by HCF:
- LCM(306, 657) = 201342 / 9 = 22374
Final Result
- The LCM of 306 and 657 is 22374.
Conclusion
- Understanding the relationship between HCF and LCM helps simplify calculations and reinforces the concepts of divisibility and multiples in mathematics.
The Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) are fundamental concepts in number theory.
Relationship Between HCF and LCM
- The relationship between HCF and LCM of two numbers can be expressed as:
LCM(a, b) = (a * b) / HCF(a, b)
Calculating LCM of 306 and 657
1. Identify the values:
- Given:
- a = 306
- b = 657
- HCF = 9
2. Calculate using the formula:
- Substitute the values into the formula:
- LCM(306, 657) = (306 * 657) / 9
3. Perform the multiplication:
- First calculate 306 * 657:
- 306 * 657 = 201342
4. Divide by HCF:
- Now divide by HCF:
- LCM(306, 657) = 201342 / 9 = 22374
Final Result
- The LCM of 306 and 657 is 22374.
Conclusion
- Understanding the relationship between HCF and LCM helps simplify calculations and reinforces the concepts of divisibility and multiples in mathematics.
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Question Description
Given that HCF 306 and 657 is 9 find LCM? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Given that HCF 306 and 657 is 9 find LCM? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that HCF 306 and 657 is 9 find LCM?.
Given that HCF 306 and 657 is 9 find LCM? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Given that HCF 306 and 657 is 9 find LCM? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that HCF 306 and 657 is 9 find LCM?.
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