Explanation

To find the L.C.M. of 12, 20, 24, and 32, we follow prime factorization:

12 = 2² × 3

20 = 2² × 5

24 = 2³ × 3

32 = 2⁵

Take the highest powers of all prime factors:

2⁵ (from 32)

3 (from 12 or 24)

5 (from 20)

Now multiply:

2⁵ × 3 × 5 = 32 × 3 × 5 = 96 × 5 = 480