MATL, 7 bytes
pG1$Zm/
Explanation
Since we can't explicitly use the builtin GCD function (Zd in MATL), I have exploited the fact that the least common multiple of a and b times the greatest common denominator of a and b is equal to the product of a and b.
p % Grab the input implicitly and multiply the two elements
G % Grab the input again, explicitly this time
1$Zm % Compute the least-common multiple
/ % Divide the two to get the greatest common denominator
Suever
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