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What is the least common multiple of 8, 9, 12 and 16?
- a)144
- b)136
- c)128
- d)120
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the least common multiple of 8, 9, 12 and 16?a)144b)136c)128d)...
The multiples of: 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136,
144, 152, ...
9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153,
...
12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, ...
16 are: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, ...
So the least common multiple of 8, 9, 12 and 16 is 144.
144, 152, ...
9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153,
...
12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, ...
16 are: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, ...
So the least common multiple of 8, 9, 12 and 16 is 144.
Most Upvoted Answer
What is the least common multiple of 8, 9, 12 and 16?a)144b)136c)128d)...
Understanding Least Common Multiple (LCM)
The least common multiple (LCM) of a set of numbers is the smallest multiple that is divisible by each of the numbers in the set. To find the LCM of 8, 9, 12, and 16, we can use the prime factorization method.
Step 1: Prime Factorization
- 8 = 2 x 2 x 2 = 2^3
- 9 = 3 x 3 = 3^2
- 12 = 2 x 2 x 3 = 2^2 x 3^1
- 16 = 2 x 2 x 2 x 2 = 2^4
Step 2: Identify the Highest Powers
Next, we take the highest power of each prime number from the factorizations:
- For 2: The highest power is 2^4 (from 16)
- For 3: The highest power is 3^2 (from 9)
Step 3: Calculate the LCM
Now, we multiply these highest powers together:
- LCM = 2^4 x 3^2
- LCM = 16 x 9
- LCM = 144
Conclusion
The least common multiple of 8, 9, 12, and 16 is 144, which corresponds to option 'A'.
Key Points:
- LCM is the smallest multiple of each number.
- Prime factorization helps in determining the LCM.
- Multiply the highest powers of all prime factors.
This systematic approach ensures that you find the least common multiple effectively!
The least common multiple (LCM) of a set of numbers is the smallest multiple that is divisible by each of the numbers in the set. To find the LCM of 8, 9, 12, and 16, we can use the prime factorization method.
Step 1: Prime Factorization
- 8 = 2 x 2 x 2 = 2^3
- 9 = 3 x 3 = 3^2
- 12 = 2 x 2 x 3 = 2^2 x 3^1
- 16 = 2 x 2 x 2 x 2 = 2^4
Step 2: Identify the Highest Powers
Next, we take the highest power of each prime number from the factorizations:
- For 2: The highest power is 2^4 (from 16)
- For 3: The highest power is 3^2 (from 9)
Step 3: Calculate the LCM
Now, we multiply these highest powers together:
- LCM = 2^4 x 3^2
- LCM = 16 x 9
- LCM = 144
Conclusion
The least common multiple of 8, 9, 12, and 16 is 144, which corresponds to option 'A'.
Key Points:
- LCM is the smallest multiple of each number.
- Prime factorization helps in determining the LCM.
- Multiply the highest powers of all prime factors.
This systematic approach ensures that you find the least common multiple effectively!
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What is the least common multiple of 8, 9, 12 and 16?a)144b)136c)128d)120Correct answer is option 'A'. Can you explain this answer? for Class 5 2025 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about What is the least common multiple of 8, 9, 12 and 16?a)144b)136c)128d)120Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 5 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least common multiple of 8, 9, 12 and 16?a)144b)136c)128d)120Correct answer is option 'A'. Can you explain this answer?.
What is the least common multiple of 8, 9, 12 and 16?a)144b)136c)128d)120Correct answer is option 'A'. Can you explain this answer? for Class 5 2025 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about What is the least common multiple of 8, 9, 12 and 16?a)144b)136c)128d)120Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 5 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least common multiple of 8, 9, 12 and 16?a)144b)136c)128d)120Correct answer is option 'A'. Can you explain this answer?.
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