The least common multiple (LCM) of 24, 32, and 16 is 96.
To find the LCM, we first need to determine the prime factorization of each number:
- 24 = 2^3 × 3
- 32 = 2^5
- 16 = 2^4
Next, we identify the highest power of each prime number present in the factorizations:
- For the prime number 2, the highest power is 2^5 (from 32).
- For the prime number 3, the highest power is 3^1 (from 24).
Now, we multiply these together to get the LCM:
LCM = 2^5 × 3^1 = 32 × 3 = 96
Thus, the least common multiple of 24, 32, and 16 is 96.