If you factor each of these numbers to their prime factors you get:
You can find the LCM by selecting all the factors except those that are duplicates.
So the LCM must have factors 2,19 in order to be divisible by 38, must have two factors of 3 and one of 5 to be divisible by 45, and must have 2 and 5 as factors to be divisible by 10, but those have already been accounted for.
That means 2 x 19 x 3 x 3 x 5 is the lowest common multiple.
Stephen La Rocque.>