Step 1: Prime Factorization
Prime factorize each number:
- \( 24 = 2^3 \times 3 \)
- \( 36 = 2^2 \times 3^2 \)
- \( 60 = 2^2 \times 3 \times 5 \)
Step 2: Identify Highest Powers of Prime Factors
Select the highest power for each unique prime factor present:
- Highest power of 2: \( 2^3 \)
- Highest power of 3: \( 3^2 \)
- Highest power of 5: \( 5^1 \)
Calculate the LCM by multiplying these highest powers:\[\text{LCM} = 2^3 \times 3^2 \times 5\]
Step 3: Final Result
The LCM of 24, 36, and 60 is \( \boxed{2^3 \times 3^2 \times 5} \).