What is the least common denominator for adding the fractions 4/15, 1/12, and 3/8

The least common denominator would be the least common multiple (LCM) of the denominators, 15 12 and 8.

To find the LCM, multiply two of the numbers together and test to see if the third one divides evenly into it.

15 x 8 = 120

120 : 12 = 10

Because all three numbers go evenly into 120 (and 120 is the smallest number for which that is true), the least common denominator would be 120.

I think you want the least common multipule (exg LCM of 2,3,4 is 12)

so we find the factors and include all of them so like this

15=3 times 5

12=2 times 2 times 3

8=2 times 2 times 2

so to include all of them we include 3 2's, 1 3 and 1 5 or 2 times 2 times 2 times 3 times 5 or 8 times 15 or 4 times 30 or 120

the LCM is 120

so 4/15=32/120

1/12=10/120

3/8=45/120

add 32/120+10/120+45/120 = (32+10+45) / 120=87/120