Find the least common multiple in each set of numbers.
1) 8,9,12,18
2) 6,8,9,27,36
I have trouble factoring the denominators in this one.
3/7 + 2/5 + 1/10
try a lcd of 70
The LCM is that smallest whole number that each of your given numbers divide into
8 = 2x2x2
9 = 3x3
12 = 2x2x3
18 = 2x3x3
so looking at those, I will need three 2' and two 3's
LCM = 2x2x2x3x3 = 72
As to your second one,
7 = 1x7
5 = 1x5
10 = 2x5
So your lowest common denominator, or the LCM, is
7x5x2 = 70
I need to rewrite the fractions so that all the denominators are the same.
To find the least common multiple (LCM) of a set of numbers, you can follow these steps:
1) Write down all the numbers in the set:
a) For the first set of numbers, you have: 8, 9, 12, and 18.
b) For the second set of numbers, you have: 6, 8, 9, 27, and 36.
2) Find the prime factorization of each number in the set:
a) For the first set of numbers:
- The prime factorization of 8 is 2^3.
- The prime factorization of 9 is 3^2.
- The prime factorization of 12 is 2^2 * 3.
- The prime factorization of 18 is 2 * 3^2.
b) For the second set of numbers:
- The prime factorization of 6 is 2 * 3.
- The prime factorization of 8 is 2^3.
- The prime factorization of 9 is 3^2.
- The prime factorization of 27 is 3^3.
- The prime factorization of 36 is 2^2 * 3^2.
3) Identify the highest power of each prime factor that appears in any of the numbers:
a) For the first set of numbers:
- The highest power of 2 is 2^3 (from 8).
- The highest power of 3 is 3^2 (from 9).
b) For the second set of numbers:
- The highest power of 2 is 2^3 (from 8).
- The highest power of 3 is 3^3 (from 27).
4) Calculate the product of the highest powers from step 3:
a) For the first set of numbers: LCM = (2^3) * (3^2) = 8 * 9 = 72.
b) For the second set of numbers: LCM = (2^3) * (3^3) = 8 * 27 = 216.
So, the least common multiple for:
1) 8, 9, 12, 18 is 72.
2) 6, 8, 9, 27, 36 is 216.
Now let's solve the fractional addition problem:
To add fractions together, you need to find a common denominator.
In this case, the denominators are 7, 5, and 10.
To find the LCM of the denominators 7, 5, and 10, follow the same steps as before:
1) Write down the numbers: 7, 5, 10.
2) Find the prime factorization of each number:
- The prime factorization of 7 is just 7.
- The prime factorization of 5 is just 5.
- The prime factorization of 10 is 2 * 5.
3) Identify the highest power of each prime factor:
- The highest power of 2 is 2^1 (from 10).
- The highest power of 5 is 5^1 (from 5).
- There is no prime factor common to all three numbers.
4) Calculate the product of the highest powers: LCM = (2^1) * (5^1) = 2 * 5 = 10.
Therefore, the least common multiple (common denominator) for 7, 5, and 10 is 10.
Now you can rewrite the fractions with a common denominator of 10:
3/7 + 2/5 + 1/10 = (3/7) * (10/10) + (2/5) * (2/2) + (1/10) = (30/70) + (4/10) + (1/10)
Simplifying the fractions:
= 30/70 + 4/10 + 1/10
= 3/7 + 2/5 + 1/10.
Now that the fractions have a common denominator, you can add them together.