Find the GCF for each of the following groups of numbers.

36, 54, and 180

Find the LCM for each of the following groups of numbers. Use whichever method you
wish.
8, 15, and 20

can anyone IM me or email how to SIMJPLIFY RADICAL EXPRESSIONS please?

To find the greatest common factor (GCF) for a group of numbers, you can use the prime factorization method. Here's how you can find the GCF for the numbers 36, 54, and 180:

Step 1: Prime factorize each number:
- 36 = 2^2 * 3^2
- 54 = 2 * 3^3
- 180 = 2^2 * 3^2 * 5

Step 2: Identify the common prime factors and their lowest exponents among the numbers:
- 2^2 * 3^2 = 36
- 2 * 3^2 = 54
- 2^2 * 3^2 = 180

Step 3: Multiply the common prime factors:
- GCF = 2^2 * 3^2 = 4 * 9 = 36

Therefore, the greatest common factor for 36, 54, and 180 is 36.

To find the least common multiple (LCM) for a group of numbers, you can also use the prime factorization method or the method of listing multiples. Here's how you can find the LCM for the numbers 8, 15, and 20:

Prime factorization method:
Step 1: Prime factorize each number:
- 8 = 2^3
- 15 = 3 * 5
- 20 = 2^2 * 5

Step 2: Identify the common prime factors and their highest exponents among the numbers:
- 2^3 = 8
- 3 = 15
- 2^2 * 5 = 20

Step 3: Multiply the common prime factors:
- LCM = 2^3 * 3 * 5 = 8 * 3 * 5 = 120

Therefore, the least common multiple for 8, 15, and 20 is 120.

Alternatively, you can also use the method of listing multiples. Find the multiples of each number until you find the smallest common multiple:
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ...
- Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
- Multiples of 20: 20, 40, 60, 80, 100, 120, ...

From the list, we can see that 120 is the smallest number that appears in all three lists, making it the least common multiple.