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The least common multiple (LCM) of 6 and 8 is:
- a)12
- b)18
- c)24
- d)48
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The least common multiple (LCM) of 6 and 8 is:a)12b)18c)24d)48Correct ...
Understanding LCM
The Least Common Multiple (LCM) of two numbers is the smallest multiple that is evenly divisible by both numbers. To find the LCM of 6 and 8, we can use various methods, including listing multiples, prime factorization, or using the relationship between GCD and LCM.
Method 1: Listing Multiples
- Multiples of 6: 6, 12, 18, 24, 30, 36, ...
- Multiples of 8: 8, 16, 24, 32, 40, ...
Now, look for the smallest common multiple in both lists. The first common multiple is 24.
Method 2: Prime Factorization
- Prime Factorization of 6: 2 × 3
- Prime Factorization of 8: 2 × 2 × 2 (or 2^3)
To find the LCM, take the highest power of each prime factor:
- For 2: The highest power is 2^3 (from 8).
- For 3: The highest power is 3^1 (from 6).
Now, multiply these together:
- LCM = 2^3 × 3^1 = 8 × 3 = 24
Conclusion
Thus, the least common multiple of 6 and 8 is 24, confirming that the correct answer is option 'C'. This method ensures that we have accurately calculated the LCM through two different approaches, making it reliable.
The Least Common Multiple (LCM) of two numbers is the smallest multiple that is evenly divisible by both numbers. To find the LCM of 6 and 8, we can use various methods, including listing multiples, prime factorization, or using the relationship between GCD and LCM.
Method 1: Listing Multiples
- Multiples of 6: 6, 12, 18, 24, 30, 36, ...
- Multiples of 8: 8, 16, 24, 32, 40, ...
Now, look for the smallest common multiple in both lists. The first common multiple is 24.
Method 2: Prime Factorization
- Prime Factorization of 6: 2 × 3
- Prime Factorization of 8: 2 × 2 × 2 (or 2^3)
To find the LCM, take the highest power of each prime factor:
- For 2: The highest power is 2^3 (from 8).
- For 3: The highest power is 3^1 (from 6).
Now, multiply these together:
- LCM = 2^3 × 3^1 = 8 × 3 = 24
Conclusion
Thus, the least common multiple of 6 and 8 is 24, confirming that the correct answer is option 'C'. This method ensures that we have accurately calculated the LCM through two different approaches, making it reliable.
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Community Answer
The least common multiple (LCM) of 6 and 8 is:a)12b)18c)24d)48Correct ...
6 = 2 × 3, 8 = 23 → LCM = 23 × 3 = 24.
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The least common multiple (LCM) of 6 and 8 is:a)12b)18c)24d)48Correct answer is option 'C'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The least common multiple (LCM) of 6 and 8 is:a)12b)18c)24d)48Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The least common multiple (LCM) of 6 and 8 is:a)12b)18c)24d)48Correct answer is option 'C'. Can you explain this answer?.
The least common multiple (LCM) of 6 and 8 is:a)12b)18c)24d)48Correct answer is option 'C'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The least common multiple (LCM) of 6 and 8 is:a)12b)18c)24d)48Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The least common multiple (LCM) of 6 and 8 is:a)12b)18c)24d)48Correct answer is option 'C'. Can you explain this answer?.
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