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Find the least number which is completely divisible by 14, 15, and 18.
- a)580
- b)720
- c)670
- d)630
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Find the least number which is completely divisible by 14, 15, and 18....
Concept:
Least number divisible by a group of numbers is given by their LCM.
Calculation:
14 = 2 × 7
15 = 5 × 3
18 = 2 × 32
LCM(14, 15, 18) = 2 × 32 × 5 × 7
LCM(14, 15, 18) = 630
∴ Least number divisible by 14, 15 and 18 is 630
Most Upvoted Answer
Find the least number which is completely divisible by 14, 15, and 18....
Finding the Least Common Multiple (LCM)
To find the least number that is completely divisible by 14, 15, and 18, we need to calculate the Least Common Multiple (LCM) of these numbers.
Step 1: Prime Factorization
- 14 = 2 × 7
- 15 = 3 × 5
- 18 = 2 × 3²
Step 2: Identify Unique Prime Factors
The unique prime factors from the factorizations are:
- 2
- 3
- 5
- 7
Step 3: Determine the Highest Powers
Next, we take the highest power of each prime factor:
- 2^1 (from 14 and 18)
- 3^2 (from 18)
- 5^1 (from 15)
- 7^1 (from 14)
Step 4: Calculate the LCM
Now, we multiply these highest powers together:
- LCM = 2^1 × 3^2 × 5^1 × 7^1
- LCM = 2 × 9 × 5 × 7
Now perform the multiplication step-by-step:
- 2 × 9 = 18
- 18 × 5 = 90
- 90 × 7 = 630
Conclusion
Thus, the least number which is completely divisible by 14, 15, and 18 is 630.
Therefore, the correct answer is option 'D'.
To find the least number that is completely divisible by 14, 15, and 18, we need to calculate the Least Common Multiple (LCM) of these numbers.
Step 1: Prime Factorization
- 14 = 2 × 7
- 15 = 3 × 5
- 18 = 2 × 3²
Step 2: Identify Unique Prime Factors
The unique prime factors from the factorizations are:
- 2
- 3
- 5
- 7
Step 3: Determine the Highest Powers
Next, we take the highest power of each prime factor:
- 2^1 (from 14 and 18)
- 3^2 (from 18)
- 5^1 (from 15)
- 7^1 (from 14)
Step 4: Calculate the LCM
Now, we multiply these highest powers together:
- LCM = 2^1 × 3^2 × 5^1 × 7^1
- LCM = 2 × 9 × 5 × 7
Now perform the multiplication step-by-step:
- 2 × 9 = 18
- 18 × 5 = 90
- 90 × 7 = 630
Conclusion
Thus, the least number which is completely divisible by 14, 15, and 18 is 630.
Therefore, the correct answer is option 'D'.
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Find the least number which is completely divisible by 14, 15, and 18.a)580b)720c)670d)630Correct answer is option 'D'. Can you explain this answer?
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Find the least number which is completely divisible by 14, 15, and 18.a)580b)720c)670d)630Correct answer is option 'D'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about Find the least number which is completely divisible by 14, 15, and 18.a)580b)720c)670d)630Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the least number which is completely divisible by 14, 15, and 18.a)580b)720c)670d)630Correct answer is option 'D'. Can you explain this answer?.
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