# A number theory problem by Christopher Boo

Today I learned that, for 2 positive integers $$a$$ and $$b,$$ $\gcd(a,b)\times \text{lcm}(a,b)=a\times b.$ Can we extend this formula to 3 positive integers as follows: $\gcd(a,b,c)\times \text{lcm}(a,b,c)=a\times b \times c?$

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