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What is the least common multiple (LCM) of 12, 15, and 20?
- a)120
- b)60
- c)180
- d)240
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
What is the least common multiple (LCM) of 12, 15, and 20?a)120b)60c)1...
LCM calculation: 2² * 3 * 5 = 60
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What is the least common multiple (LCM) of 12, 15, and 20?a)120b)60c)1...
Understanding LCM
The Least Common Multiple (LCM) of a set of numbers is the smallest multiple that is common to all the numbers. To find the LCM of 12, 15, and 20, we can use the prime factorization method.
Step 1: Prime Factorization
- For 12:
- 12 = 2 × 2 × 3 = 2² × 3¹
- For 15:
- 15 = 3 × 5 = 3¹ × 5¹
- For 20:
- 20 = 2 × 2 × 5 = 2² × 5¹
Step 2: Identify the Highest Powers
Next, we identify the highest power of each prime number involved:
- The prime factors are 2, 3, and 5.
- The highest power of 2: 2² (from 12 and 20)
- The highest power of 3: 3¹ (from 12 and 15)
- The highest power of 5: 5¹ (from 15 and 20)
Step 3: Calculate the LCM
Now, we multiply these highest powers together:
- LCM = 2² × 3¹ × 5¹
- LCM = 4 × 3 × 5
- LCM = 12 × 5
- LCM = 60
Conclusion
The LCM of 12, 15, and 20 is 60. However, it seems there was a mistake in the provided answer options. The correct answer is 60. If the correct answer indicated was option 'B' (120), please verify the options provided, as our calculations confirm that the LCM is indeed 60.
The Least Common Multiple (LCM) of a set of numbers is the smallest multiple that is common to all the numbers. To find the LCM of 12, 15, and 20, we can use the prime factorization method.
Step 1: Prime Factorization
- For 12:
- 12 = 2 × 2 × 3 = 2² × 3¹
- For 15:
- 15 = 3 × 5 = 3¹ × 5¹
- For 20:
- 20 = 2 × 2 × 5 = 2² × 5¹
Step 2: Identify the Highest Powers
Next, we identify the highest power of each prime number involved:
- The prime factors are 2, 3, and 5.
- The highest power of 2: 2² (from 12 and 20)
- The highest power of 3: 3¹ (from 12 and 15)
- The highest power of 5: 5¹ (from 15 and 20)
Step 3: Calculate the LCM
Now, we multiply these highest powers together:
- LCM = 2² × 3¹ × 5¹
- LCM = 4 × 3 × 5
- LCM = 12 × 5
- LCM = 60
Conclusion
The LCM of 12, 15, and 20 is 60. However, it seems there was a mistake in the provided answer options. The correct answer is 60. If the correct answer indicated was option 'B' (120), please verify the options provided, as our calculations confirm that the LCM is indeed 60.
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What is the least common multiple (LCM) of 12, 15, and 20?a)120b)60c)180d)240Correct answer is option 'B'. Can you explain this answer? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about What is the least common multiple (LCM) of 12, 15, and 20?a)120b)60c)180d)240Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least common multiple (LCM) of 12, 15, and 20?a)120b)60c)180d)240Correct answer is option 'B'. Can you explain this answer?.
What is the least common multiple (LCM) of 12, 15, and 20?a)120b)60c)180d)240Correct answer is option 'B'. Can you explain this answer? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about What is the least common multiple (LCM) of 12, 15, and 20?a)120b)60c)180d)240Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least common multiple (LCM) of 12, 15, and 20?a)120b)60c)180d)240Correct answer is option 'B'. Can you explain this answer?.
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