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The LCM of 15, 18, and 20 is 180.
To arrive at an LCM we need to factorize the candidate numbers, and then ensure that each factor is included in the factors which will create the LCM
The prime factors of 20 are 2, 2 and 5 so all of those must be in the LCM
The factors of 15 are 3 and 5. As we have a 5 already we only need to add the 3 to the list.
Now we have 2, 2, 3 and 5
The factors of 18 are 2, 3 and 3.
As we have a 2 and one 3 already, we need to add the second three to the list..... this gives us
2, 2, 3, 3 and 5 as the factors that will give us the LCM
Multiplying these together we get 180
180 / 20 = 9
180 / 15 = 12
180 / 18 = 10
As 9, 12 and 10 don't share any factors we can see that 180 is indeed the LCM of the three numbers we were given.
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