## The logic used in the given solutions is correct. Let me explain how to find the LCM and GCF of the given numbers:

(1) Finding the LCM:

To find the LCM (Least Common Multiple) of the numbers 5, 15, and 20, you can use the prime factorization method.

First, factorize each number into its prime factors:

5 = 5 (since 5 is a prime number)

15 = 3 Ã— 5

20 = 2 Ã— 2 Ã— 5

Next, you take the highest power of each prime factor that appears in any of the numbers. In this case, the prime factors are 2, 3, and 5.

2 appears twice in the factorization of 20, so we take 2^2.

3 appears once in the factorization of 15, so we take 3^1.

5 appears once in the factorization of 15 and 20, so we take 5^1.

Multiplying these together, we get:

LCM = 2^2 Ã— 3^1 Ã— 5^1 = 4 Ã— 3 Ã— 5 = 60.

So, the correct LCM of 5, 15, and 20 is 60. Your calculation of 120 is incorrect.

(2) Finding the GCF:

To find the GCF (Greatest Common Factor) of the numbers 36, 64, and 180, you can again use the prime factorization method.

Factorize each number into its prime factors:

36 = 2 Ã— 2 Ã— 3 Ã— 3

64 = 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2

180 = 2 Ã— 2 Ã— 3 Ã— 3 Ã— 5

Now, you look for the common prime factors among these numbers.

The common prime factors are:

2 appears twice in the factorization of 36 and 64, but only once in the factorization of 180.

So, we take 2 Ã— 2 = 4.

The GCF is 4.

Therefore, your calculation of GCF=4 is correct.