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What will be the least number which when doubled will be exactly divisible by 12,18,21 and 30?
- a)630
- b)360
- c)603
- d)306
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
What will be the least number which when doubled will be exactly divis...
LCM of 12,18,21 and 30 = 1260
Doubled (divide by 2) = 1260/2 = 630
Doubled (divide by 2) = 1260/2 = 630
Most Upvoted Answer
What will be the least number which when doubled will be exactly divis...
Approach:
To find the least number which when doubled will be exactly divisible by 12, 18, 21, and 30, we need to find the least common multiple (LCM) of these numbers and then double it.
Solution:
Finding LCM of 12, 18, 21, and 30:
- Prime factorization of the given numbers:
- 12 = 2^2 * 3
- 18 = 2 * 3^2
- 21 = 3 * 7
- 30 = 2 * 3 * 5
- LCM will have the highest power of each prime factor:
- LCM(12, 18, 21, 30) = 2^2 * 3^2 * 5 * 7 = 2^2 * 3^2 * 5 * 7 = 2 * 3^2 * 5 * 7 = 630
Least number that is exactly divisible by 12, 18, 21, and 30:
- The least number that is exactly divisible by the LCM is the LCM itself.
- So, the least number that when doubled will be exactly divisible by 12, 18, 21, and 30 is 630.
Therefore, the correct answer is option A) 630.
To find the least number which when doubled will be exactly divisible by 12, 18, 21, and 30, we need to find the least common multiple (LCM) of these numbers and then double it.
Solution:
Finding LCM of 12, 18, 21, and 30:
- Prime factorization of the given numbers:
- 12 = 2^2 * 3
- 18 = 2 * 3^2
- 21 = 3 * 7
- 30 = 2 * 3 * 5
- LCM will have the highest power of each prime factor:
- LCM(12, 18, 21, 30) = 2^2 * 3^2 * 5 * 7 = 2^2 * 3^2 * 5 * 7 = 2 * 3^2 * 5 * 7 = 630
Least number that is exactly divisible by 12, 18, 21, and 30:
- The least number that is exactly divisible by the LCM is the LCM itself.
- So, the least number that when doubled will be exactly divisible by 12, 18, 21, and 30 is 630.
Therefore, the correct answer is option A) 630.
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