Find the LCM using the prime factorization method: 48,64,72,96,108.

To find the Least Common Multiple (LCM) using the prime factorization method for the numbers 48, 64, 72, 96, and 108, follow these steps:

Step 1: Find the Prime Factorization of Each Number
48 = 2^4 * 3
64 = 2^6
72 = 2^3 * 3^2
96 = 2^5 * 3
108 = 2^2 * 3^3
Step 2: Identify the Highest Powers of Each Prime Factor
The prime factors involved are 2 and 3.
The highest power of 2 is 2^6 (from 64).
The highest power of 3 is 3^3 (from 108).
Step 3: Multiply the Highest Powers of Each Prime Factor
Multiply the highest powers of 2 and 3:
LCM = 2^6 * 3^3
Step 4: Calculate the Value
2^6 = 64
3^3 = 27
Multiply 64 by 27:
LCM = 64 * 27 = 1728
Final Answer:
The LCM of 48, 64, 72, 96, and 108 is 1728.