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What will be the least number which when doubled will be exactly divisible by 12, 14, 16 and 18?
- a)636
- b)428
- c)504
- d)226
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What will be the least number which when doubled will be exactly divis...
Calculation:
Let the least number = a
When we doubled the number it becomes 2a
Now, 2a is exactly divisible by 12, 14, 16 and 18
⇒ 2a = 1008 (LCM of 12, 14, 16 and 18 = 1008)
⇒
a = 504∴ The correct answer is 504.
Most Upvoted Answer
What will be the least number which when doubled will be exactly divis...
Understanding the Problem
To find the least number which when doubled is exactly divisible by 12, 14, 16, and 18, we need to first determine the least common multiple (LCM) of these numbers.
Step 1: Prime Factorization
- 12 = 2² * 3
- 14 = 2 * 7
- 16 = 2⁴
- 18 = 2 * 3²
Step 2: Finding the LCM
The LCM is calculated by taking the highest power of each prime factor:
- For 2: The highest power is 2⁴ (from 16)
- For 3: The highest power is 3² (from 18)
- For 7: The highest power is 7¹ (from 14)
Step 3: Calculate the LCM
Now, we can find the LCM:
- LCM = 2⁴ * 3² * 7¹
- LCM = 16 * 9 * 7
- LCM = 144 * 7 = 1008
Step 4: Finding the Original Number
Since we want a number that, when doubled, is divisible by the LCM, we can set up the equation:
- Let the required number be x.
- 2x = 1008 → x = 1008 / 2 = 504
Conclusion
The least number which when doubled is exactly divisible by 12, 14, 16, and 18 is therefore:
- Answer: 504 (Option C)
This calculation shows that option C is correct, confirming the requirement of divisibility for all the given numbers.
To find the least number which when doubled is exactly divisible by 12, 14, 16, and 18, we need to first determine the least common multiple (LCM) of these numbers.
Step 1: Prime Factorization
- 12 = 2² * 3
- 14 = 2 * 7
- 16 = 2⁴
- 18 = 2 * 3²
Step 2: Finding the LCM
The LCM is calculated by taking the highest power of each prime factor:
- For 2: The highest power is 2⁴ (from 16)
- For 3: The highest power is 3² (from 18)
- For 7: The highest power is 7¹ (from 14)
Step 3: Calculate the LCM
Now, we can find the LCM:
- LCM = 2⁴ * 3² * 7¹
- LCM = 16 * 9 * 7
- LCM = 144 * 7 = 1008
Step 4: Finding the Original Number
Since we want a number that, when doubled, is divisible by the LCM, we can set up the equation:
- Let the required number be x.
- 2x = 1008 → x = 1008 / 2 = 504
Conclusion
The least number which when doubled is exactly divisible by 12, 14, 16, and 18 is therefore:
- Answer: 504 (Option C)
This calculation shows that option C is correct, confirming the requirement of divisibility for all the given numbers.
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What will be the least number which when doubled will be exactly divisible by 12, 14, 16 and 18?a)636b)428c)504d)226Correct answer is option 'C'. Can you explain this answer?
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