Find the L.C.M of the given numbers by prime factorization method: 36, 40, 126

To find the LCM (Least Common Multiple) of the given numbers 36, 40, and 126 using the prime factorization method, follow these steps:

Step 1: Find the prime factors of each number.
Step 2: Identify the highest power of each prime factor that appears in any of the numbers.
Step 3: Multiply these highest powers to get the LCM.

Let's start with the prime factorization of each number:

Prime factorization of 36:
36 = 2^2 * 3^2

Prime factorization of 40:
40 = 2^3 * 5^1

Prime factorization of 126:
126 = 2^1 * 3^2 * 7^1

Now, let's identify the highest power of each prime factor:

The highest power of 2 is 2^3.
The highest power of 3 is 3^2.
The highest power of 5 is 5^1.
The highest power of 7 is 7^1.
Now, multiply these highest powers together to find the LCM:

LCM = 2^3 * 3^2 * 5^1 * 7^1

LCM = 8 * 9 * 5 * 7

LCM = 2520

So, the LCM of 36, 40, and 126 is 2520.