What is the least common multiple of 12, 15 and 18

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.

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