If a, b are integers such that a > b then lcm(a, b) lies in _________Optionsa > lcm(a, b) > ba > b > lcm(a, b)lcm(a, b) >= a > bNone of these
Question
If a, b are integers such that a > b then lcm(a, b) lies in _________Optionsa > lcm(a, b) > ba > b > lcm(a, b)lcm(a, b) >= a > bNone of these
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) cannot be less than a. This is because a is a multiple of itself and therefore, the smallest number that is a multiple of a (and any other number) is a itself.
Therefore, the lcm(a, b) is either equal to a (when a is a multiple of b) or greater than a (when a is not a multiple of b).
So, the correct relation is lcm(a, b) >= a > b.
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