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30 = 2*3 *5
18 = 2*3*3
The LCM of 30 and 18 = 2*3*3*5 = 90 (<-- For 2, I have only one choice. For 3, I pick the higher number 3*3. For 5, there is only one choice.)
Reasoning:
The multiples of 30 are 30, 60, 90, 120, ...
The multiples of 18 are 18, 36, 54, 72, 90, 108, ...
The smallest common factor of the two integers is 90.
Q.E.D.
==============================
The Least Common Multiple of 30 18 is 90.
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