Prime Factorization

Break down each number into its prime factors: $36 = 2^2 \times 3^2$, $54 = 2^1 \times 3^3$, $72 = 2^3 \times 3^2$, $96 = 2^5 \times 3^1$.

$36 = 2^2 \times 3^2, \; 54 = 2 \times 3^3, \; 72 = 2^3 \times 3^2, \; 96 = 2^5 \times 3$

Identify Maximum Powers

Collect the highest power for each prime base (2 and 3) found in the factorizations: For prime 2, the max power is $2^5$. For prime 3, the max power is $3^3$.

$2^5 \; \text{and} \; 3^3$

Calculate LCM

Multiply the highest powers together to get the LCM: $2^5 \times 3^3 = 32 \times 27$.

$32 \times 27 = 864$