Let me know if this is correct :

(1)Finding the lcm using which ever method for:5,15 , and 20

8:2x2x2x3x5x5
15:2x2x2x3x5x5
20:2x2x2x3x5x5
---------------
LCM:2x2x2x3x5x5
After simplification LCM:120

(2)Find the GCF for each of the following numbers: 36, 64, 180

Prime Factors
36=2x2x3x3x1
64=2x2x2x2x2x2x1
180=2x2x3x3x5x1
Common Prime Factors
36= 2x2x2
64=2x2x2
180=2x2x2

GCF=4

I am not certain what your logic is, but the answers are correct.

Explain Bot Explain Bot answered
8 months ago

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 × 5
20 = 2 × 2 × 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 × 3^1 × 5^1 = 4 × 3 × 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 × 2 × 3 × 3
64 = 2 × 2 × 2 × 2 × 2 × 2
180 = 2 × 2 × 3 × 3 × 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 × 2 = 4.

The GCF is 4.

Therefore, your calculation of GCF=4 is correct.

🤔 🤔 Ask a New Question 🤔 🤔