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What is the least number which is divisible by 2, 3, 7, 12, 16, 18 and 30?
- a)3040
- b)4050
- c)5040
- d)5120
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What is the least number which is divisible by 2, 3, 7, 12, 16, 18 and...
LCM of 2, 3, 7, 12, 16, 18, 30 = 5040
Most Upvoted Answer
What is the least number which is divisible by 2, 3, 7, 12, 16, 18 and...
To find the least number that is divisible by 2, 3, 7, 12, 16, 18, and 30, we need to find the least common multiple (LCM) of these numbers.
Step 1: Prime Factorization
We start by finding the prime factorization of each number:
- 2 = 2
- 3 = 3
- 7 = 7
- 12 = 2 × 2 × 3
- 16 = 2 × 2 × 2 × 2
- 18 = 2 × 3 × 3
- 30 = 2 × 3 × 5
Step 2: Find the Highest Power of Each Prime Factor
Next, we identify the highest power of each prime factor present in any of the numbers. The LCM will be the product of these highest powers.
- The highest power of 2 is 2 × 2 × 2 × 2 = 16.
- The highest power of 3 is 3 × 3 = 9.
- The highest power of 7 is 7.
- The highest power of 5 is 5.
Step 3: Calculate the LCM
Finally, we calculate the LCM by multiplying the highest powers of each prime factor:
LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7
LCM = 16 × 9 × 5 × 7
LCM = 5040
Therefore, the least number that is divisible by 2, 3, 7, 12, 16, 18, and 30 is 5040. This corresponds to option 'C'.
Step 1: Prime Factorization
We start by finding the prime factorization of each number:
- 2 = 2
- 3 = 3
- 7 = 7
- 12 = 2 × 2 × 3
- 16 = 2 × 2 × 2 × 2
- 18 = 2 × 3 × 3
- 30 = 2 × 3 × 5
Step 2: Find the Highest Power of Each Prime Factor
Next, we identify the highest power of each prime factor present in any of the numbers. The LCM will be the product of these highest powers.
- The highest power of 2 is 2 × 2 × 2 × 2 = 16.
- The highest power of 3 is 3 × 3 = 9.
- The highest power of 7 is 7.
- The highest power of 5 is 5.
Step 3: Calculate the LCM
Finally, we calculate the LCM by multiplying the highest powers of each prime factor:
LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7
LCM = 16 × 9 × 5 × 7
LCM = 5040
Therefore, the least number that is divisible by 2, 3, 7, 12, 16, 18, and 30 is 5040. This corresponds to option 'C'.
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What is the least number which is divisible by 2, 3, 7, 12, 16, 18 and 30?a)3040b)4050c)5040d)5120Correct answer is option 'C'. 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 number which is divisible by 2, 3, 7, 12, 16, 18 and 30?a)3040b)4050c)5040d)5120Correct answer is option 'C'. 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 number which is divisible by 2, 3, 7, 12, 16, 18 and 30?a)3040b)4050c)5040d)5120Correct answer is option 'C'. Can you explain this answer?.
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