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If positive integer n is divisible by both 4 and 21, then n must be divisible by which of the following?
- a)8
- b)12
- c)18
- d)24
- e)48
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If positive integer n is divisible by both 4 and 21, then n must be di...
If n is divisible by both 4 and 21, its prime factors include 2, 2, 3, and 7. Therefore, any integer that can be constructed as the product of these prime factors is also a factor of n. In this case, 12 is the only integer that can definitively be constructed from the prime factors of n, since 12 = 2 x 2 x 3.
The correct answer is B.
Most Upvoted Answer
If positive integer n is divisible by both 4 and 21, then n must be di...
To determine which of the given options is divisible by both 4 and 21, we need to find the least common multiple (LCM) of 4 and 21.
Finding the LCM:
The prime factors of 4 are 2 and 2, and the prime factors of 21 are 3 and 7. To find the LCM, we need to take the highest power of each prime factor:
4 = 2^2
21 = 3 * 7
Since the highest power of 2 is 2^2, and the highest power of 3 and 7 are 1, the LCM of 4 and 21 is:
LCM(4, 21) = 2^2 * 3 * 7 = 84
Therefore, any positive integer divisible by both 4 and 21 must also be divisible by 84.
Analyzing the given options:
a) 8: 8 is not divisible by 21, so it cannot be the correct answer.
b) 12: 12 is divisible by 4, but not by 21, so it cannot be the correct answer.
c) 18: 18 is not divisible by 4, so it cannot be the correct answer.
d) 24: 24 is divisible by 4, but not by 21, so it cannot be the correct answer.
e) 48: 48 is divisible by 4, but not by 21, so it cannot be the correct answer.
Therefore, the correct answer is option B, 12, as it is divisible by both 4 and 21.
Finding the LCM:
The prime factors of 4 are 2 and 2, and the prime factors of 21 are 3 and 7. To find the LCM, we need to take the highest power of each prime factor:
4 = 2^2
21 = 3 * 7
Since the highest power of 2 is 2^2, and the highest power of 3 and 7 are 1, the LCM of 4 and 21 is:
LCM(4, 21) = 2^2 * 3 * 7 = 84
Therefore, any positive integer divisible by both 4 and 21 must also be divisible by 84.
Analyzing the given options:
a) 8: 8 is not divisible by 21, so it cannot be the correct answer.
b) 12: 12 is divisible by 4, but not by 21, so it cannot be the correct answer.
c) 18: 18 is not divisible by 4, so it cannot be the correct answer.
d) 24: 24 is divisible by 4, but not by 21, so it cannot be the correct answer.
e) 48: 48 is divisible by 4, but not by 21, so it cannot be the correct answer.
Therefore, the correct answer is option B, 12, as it is divisible by both 4 and 21.
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If positive integer n is divisible by both 4 and 21, then n must be divisible by which of the following?a)8b)12c)18d)24e)48Correct answer is option 'B'. Can you explain this answer?
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