MathDB
gcd and lcm

Source: Taiwan 1st TST, final exam, second day, problem 6

August 12, 2005
number theorygreatest common divisorleast common multiplenumber theory proposed

Problem Statement

Find all positive integer triples (x,y,z)(x,y,z) such that x<y<zx<y<z, gcd⁡(x,y)=6\gcd (x,y)=6, gcd⁡(y,z)=10\gcd (y,z)=10, gcd⁡(x,z)=8\gcd (x,z)=8, and lcm(x,y,z)=2400(x,y,z)=2400. Note that the problems of the TST are not arranged in difficulty (Problem 1 of day 1 was probably the most difficult!)
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