If a, b are integers such that a > b then lcm(a, b) lies in _________ a>lcm(a, b)>b a>b>lcm(a, b) lcm(a, b)>=a>b none of the mentioned
Question
If a, b are integers such that a > b then lcm(a, b) lies in _________ a>lcm(a, b)>b a>b>lcm(a, b) lcm(a, b)>=a>b none of the mentioned
Solution
The correct answer is "lcm(a, b)>=a>b".
Here's why:
The least common multiple (lcm) of two integers a and b is the smallest positive integer that is divisible by both a and b.
Given that a > b, the lcm(a, b) could be a itself (when a is a multiple of b) or a multiple of a (when a and b have no common factors other than 1).
Therefore, the lcm(a, b) is always greater than or equal to a, and since a > b, it follows that lcm(a, b) >= a > b.
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