Find the LCM of Denominators: 8, 16, and 20

Question

What is the least common multiple of these denominators?

8   16   20 \boxed{8}~~~\boxed{16} ~~~\boxed{20}

Step-by-Step Solution

To find the least common multiple (LCM) of 8 8 , 16 16 , and 20 20 , find their prime factorizations:

8=23 8 = 2^3

16=24 16 = 2^4

20=22×5 20 = 2^2 \, \times \, 5

The LCM is obtained by taking the highest power of each prime number:

24 2^4 from 16 and 5 5 from 20.

The LCM is 24×5=16×5=80 2^4 \, \times \, 5 = 16 \, \times \, 5 = 80 .

Answer

80