As a first step you need to find the factors of the numbers
25 = 5*5
63 = 9*7
The lowest common multiple must include factors so that each of the original numbers can be created out if it. In this case we get 5*5*9*7 =1575
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32 = 2*2*2*2*2
15 = 5*3
So LCM is 2*2*2*2*2*5*3 = 480
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12 = 2*2*3 = 2*(2*3)
30 = 2*3*5 = 5*(2*3)
In this case, both numbers are multiples of 6, so we only need to include 6 once.
LCM 2*5*(2*3) = 60
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I hope this is not too confusing