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Find the number of pairs of positive integers (a,b)(a,b)(a,b) with 1≤a<b≤1001\leq a < b \leq 1001≤a<b≤100 such that
there is at least one positive integer mmm with a<m<ba<m<ba<m<b such that mmm is divisible by every common divisor of aaa and b.b.b.
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