Why is the lcm of 5 9 and 12 180 not 540?

Answer 1

Both 180 and 540 are common multiples of 5, 9 and 12. That is to say they are in the 5-times table, the 9-times table and the 12-times table.

But the L in LCM stands for Least. So, since 180 is less than 540, the LCM cannot be 540. You may like to check, for yourself, that no number smaller than 180 is in all the three tables.

Answer 2

Because it's the least common multiple. 180 and 540 are both common multiples, but 180 is less than 540.