ChallengeMediumHard Number Theory ShareHard Number Theory · Medium problemHow many ordered triples (a,b,c)(a,b,c)(a,b,c) of positive integers satisfy lcm(a,b)=1000\operatorname{lcm}(a,b)=1000lcm(a,b)=1000, lcm(b,c)=2000\operatorname{lcm}(b,c)=2000lcm(b,c)=2000, and lcm(a,c)=2000\operatorname{lcm}(a,c)=2000lcm(a,c)=2000?Check Show answer Walk through it step by step Practice more like this Review this concept