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Which of the following can be the least common multiple of two distinct integers a and b?
- a)a
- b)b
- c)a - b
- d)a + b
Correct answer is option 'D'. Can you explain this answer?
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Which of the following can be the least common multiple of two distinc...
Explanation:
The least common multiple (LCM) of two distinct integers a and b is the smallest positive integer that is divisible by both a and b.
To find the LCM of two numbers, we need to find the prime factorization of each number and then take the highest power of each prime factor that appears in either factorization.
For example, let's say we want to find the LCM of 12 and 18:
- The prime factorization of 12 is 2^2 x 3
- The prime factorization of 18 is 2 x 3^2
To find the LCM, we take the highest power of each prime factor:
- The highest power of 2 is 2^2
- The highest power of 3 is 3^2
Therefore, the LCM of 12 and 18 is 2^2 x 3^2 = 36.
Now, let's look at the answer choices:
a) a: This cannot be the LCM unless b = 1.
b) b: This cannot be the LCM unless a = 1.
c) a - b: This cannot be the LCM unless a and b are consecutive integers.
d) ab: This is a possible LCM because it is divisible by both a and b, and it is the smallest possible product of a and b that is divisible by both a and b.
Therefore, the correct answer is option D: ab.
The least common multiple (LCM) of two distinct integers a and b is the smallest positive integer that is divisible by both a and b.
To find the LCM of two numbers, we need to find the prime factorization of each number and then take the highest power of each prime factor that appears in either factorization.
For example, let's say we want to find the LCM of 12 and 18:
- The prime factorization of 12 is 2^2 x 3
- The prime factorization of 18 is 2 x 3^2
To find the LCM, we take the highest power of each prime factor:
- The highest power of 2 is 2^2
- The highest power of 3 is 3^2
Therefore, the LCM of 12 and 18 is 2^2 x 3^2 = 36.
Now, let's look at the answer choices:
a) a: This cannot be the LCM unless b = 1.
b) b: This cannot be the LCM unless a = 1.
c) a - b: This cannot be the LCM unless a and b are consecutive integers.
d) ab: This is a possible LCM because it is divisible by both a and b, and it is the smallest possible product of a and b that is divisible by both a and b.
Therefore, the correct answer is option D: ab.
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Community Answer
Which of the following can be the least common multiple of two distinc...
The least common multiple (LCM) of two distinct positive integers a and b cannot be a + b.
Instead, it is the smallest number that is a multiple of both a and b, which is either a or b if one divides the other.
Instead, it is the smallest number that is a multiple of both a and b, which is either a or b if one divides the other.
Hence , Option D is correct.
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Which of the following can be the least common multiple of two distinct integers a and b?a)ab)bc)a - bd)a + bCorrect answer is option 'D'. Can you explain this answer?
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