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Which of the following CANNOT be the least common multiple of two integers a and b, where a and b are both greater than 1?
- a)1
- b)a
- c)b
- d)a + b
Correct answer is option 'A'. Can you explain this answer?
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Which of the following CANNOT be the least common multiple of two inte...
Explanation:
Definition of LCM: The least common multiple (LCM) of two integers a and b is the smallest positive integer that is divisible by both a and b.
To find the LCM of two integers a and b, we need to find their prime factorizations. Then, the LCM is the product of the highest powers of all the prime factors. For example, the LCM of 12 and 18 is 36, because 12 = 2^2 × 3 and 18 = 2 × 3^2, and the highest powers of 2 and 3 are 2^2 and 3^2, respectively, which give 36 when multiplied together.
Now, let's consider the given options:
a) 1: 1 cannot be the LCM of any two integers greater than 1, because any positive integer greater than 1 is divisible by 1.
b) a: It is possible for a to be the LCM of two integers. For example, if a = 4 and b = 8, then the LCM is 8, which is equal to b.
c) b: It is possible for b to be the LCM of two integers. For example, if a = 6 and b = 3, then the LCM is 6, which is equal to a.
d) ab: It is possible for ab to be the LCM of two integers. For example, if a = 4 and b = 6, then the LCM is 12, which is equal to ab.
Therefore, the only option that cannot be the LCM of two integers greater than 1 is 1. So, the correct answer is option A.
Definition of LCM: The least common multiple (LCM) of two integers a and b is the smallest positive integer that is divisible by both a and b.
To find the LCM of two integers a and b, we need to find their prime factorizations. Then, the LCM is the product of the highest powers of all the prime factors. For example, the LCM of 12 and 18 is 36, because 12 = 2^2 × 3 and 18 = 2 × 3^2, and the highest powers of 2 and 3 are 2^2 and 3^2, respectively, which give 36 when multiplied together.
Now, let's consider the given options:
a) 1: 1 cannot be the LCM of any two integers greater than 1, because any positive integer greater than 1 is divisible by 1.
b) a: It is possible for a to be the LCM of two integers. For example, if a = 4 and b = 8, then the LCM is 8, which is equal to b.
c) b: It is possible for b to be the LCM of two integers. For example, if a = 6 and b = 3, then the LCM is 6, which is equal to a.
d) ab: It is possible for ab to be the LCM of two integers. For example, if a = 4 and b = 6, then the LCM is 12, which is equal to ab.
Therefore, the only option that cannot be the LCM of two integers greater than 1 is 1. So, the correct answer is option A.
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Which of the following CANNOT be the least common multiple of two inte...
If a & b is greater than 1 then it can be taken as common of a,b
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Which of the following CANNOT be the least common multiple of two integers a and b, where a and b are both greater than 1?a)1b)ac)bd)a + bCorrect answer is option 'A'. Can you explain this answer?
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