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59th Ukrainian National Mathematical Olympiad

Ukraine number theory

Problem

Given positive integers , , , such that . Is it possible for the least common multiple of and to be greater than the least common multiple of and ?
Solution
Let , , then . We will choose the other two numbers such that : , .
Final answer
Yes; for example, a=8, b=9, c=10, d=25 gives lcm(a,b)=72 and lcm(c,d)=50.

Techniques

Least common multiples (lcm)