Answer :

altavistard
Factor 12, 15 and 18:  
12=(2*3*2) or 4*3
15=3*5
 18=3*6
The largest common multiple of 12, 15 and 18 is thus 3; this is the largest factor that will divide evenly into 12, 15 and 18.
DeanR

12 = 2 × 2 × 3

15 = 3 × 5

18 = 2 × 3 × 3

We need enough factors of 2,3, and 5 to cover all the factors in each input, i.e. the maximum power of each prime factor gets multiplied to form the LCM.

The max powers are: 12 has 2 twos, 15 has 1 five and 18 as 2 threes.

LCM = 2 × 2 × 5 × 3 × 3 = 180

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