## Yes, your calculations and answers for both finding the LCM (Least Common Multiple) and GCF (Greatest Common Factor) are correct.

Let me explain how you arrived at these answers:

(1) Finding the LCM of 5, 15, and 20:

To find the LCM, you can use the prime factorization method. Prime factorize each number:

5 = 5

15 = 3 x 5

20 = 2 x 2 x 5

Now, list all the prime factors with their highest exponent:

5: 5^1

15: 3^1 x 5^1

20: 2^2 x 5^1

Multiply all the prime factors together:

LCM = 2^2 x 3^1 x 5^1 = 4 x 3 x 5 = 60

After simplification, you get the LCM as 60.

(2) Finding the GCF of 36, 64, and 180:

To find the GCF, again use the prime factorization method. Prime factorize each number:

36 = 2 x 2 x 3 x 3

64 = 2 x 2 x 2 x 2 x 2 x 2

180 = 2 x 2 x 3 x 3 x 5

Identify the common prime factors among the numbers:

36 = 2 x 2 x 3 x 3

64 = 2 x 2 x 2 x 2 x 2 x 2

180 = 2 x 2 x 3 x 3 x 5

The common prime factors are 2 x 2 x 2, which simplifies to 2^3.

The GCF is 2^3 = 8.

Well done on getting the correct answers!