3. The notion of greatest common divisor can be compared to the notion of least common multiple.
We say that m is the least common multiple of integers a and b, written m = lcm(a, b), if and only if
i. $a|m$ and $b|m$ and
ii. If $a|n$ and $b|n$, then $m ? n$.
Fill in the following table (or one like it on your own paper) with different a and b values in order to
determine a relationship between lcm(a, b) and gcd(a, b). Use the notion of prime factorizations to
prove your conjecture is always true.
a
b
a \cdot b
gcd(a, b)
lcm(a, b)
gcd(a, b) \cdot lcm(a, b)