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Found problems: 51

2015 Junior Balkan Team Selection Tests - Moldova, 8
Tags: least common multiple , lcm , number theory
Determine the number of all ordered triplets of positive integers $(a, b, c)$, which satisfy the equalities: $$[a, b] =1000, [b, c] = 2000, [c, a] =2000.$$ ([x, y]represents the least common multiple of positive integers x,y)