The LCM of these three numbers is 60. The GCF is 1. If you add the numbers, the sum is 15. Select the three numbers from the following options: 2, 6, 5, 8, 4 Show your work!
All three numbers must be factors of 60; 8 is not a factor of 60 so it can be excluded.
The numbers left are 2, 4, 5, 6
You must take the three greatest to get a sum of 15: 4+5+6 = 15
and 60 is the GCF of 4, 5, 6
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To find the three numbers that satisfy the given conditions, we need to evaluate all possible combinations. Let's go step by step:
1. Start by finding all the factors of 60. The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
2. Since the GCF of the three numbers is 1, none of the numbers can have any common factors other than 1.
3. Now, let's sum up the three numbers and check if it equals 15. We will use a trial-and-error method for this.
a. First, let's select 2 as one of the numbers. Now we need to find two more numbers whose GCF is 1, and when added to 2, the sum is 15. We can choose 6 and 7 (since 6 + 7 = 13) or 8 and 5 (since 8 + 5 = 13). But neither of these combinations equals 15. So, 2 cannot be one of the numbers.
b. Next, let's try 6 as one of the numbers. We need to find two more numbers whose GCF is 1, and when added to 6, the sum is 15. We can try 2 and 7 (since 2 + 7 = 9) or 4 and 5 (since 4 + 5 = 9). Again, neither of these combinations equals 15. So, 6 cannot be one of the numbers either.
c. Now, let's attempt 5 as one of the numbers. We need to find two more numbers whose GCF is 1, and when added to 5, the sum is 15. We can try 2 and 8 (since 2 + 8 = 10) or 4 and 6 (since 4 + 6 = 10). None of these combinations equals 15. So, 5 cannot be one of the numbers.
d. Finally, let's try 8 as one of the numbers. We need to find two more numbers whose GCF is 1, and when added to 8, the sum is 15. The only combination left is 2 and 5 (since 2 + 5 = 7), and this satisfies the conditions since the sum is 15. Therefore, the three numbers are 8, 2, and 5.
Hence, the three numbers that satisfy the given conditions are 8, 2, and 5.