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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