3. Find the LCM for the following set of numbers.
100 126 250
The prime factorization of each number is:
100 = 2^2 * 5^2
126 = 2 * 3^2 * 7
250 = 2 * 5^3
To find the LCM, we need to choose the highest power of each prime factor that appears in any of the numbers. So, the LCM would be:
2^2 * 3^2 * 5^3 * 7 = 1800
To find the least common multiple (LCM) of a set of numbers, you can use the prime factorization method. Here are the steps:
Step 1: Find the prime factorization of each number in the set.
100 = 2^2 * 5^2
126 = 2 * 3^2 * 7
250 = 2 * 5^3
Step 2: Identify the highest powers of all the prime factors that appear in any of the prime factorizations.
The highest power of 2 is 2^2.
The highest power of 3 is 3^2.
The highest power of 5 is 5^3.
The highest power of 7 is 7^1.
Step 3: Multiply all the highest powers identified in Step 2.
2^2 * 3^2 * 5^3 * 7^1 = 9000
So, the LCM for the set of numbers 100, 126, and 250 is 9000.
To find the least common multiple (LCM) for a set of numbers, we will first find the prime factorization of each number. Then, we will multiply together the highest powers of all the prime factors.
Let's find the prime factorization of each number:
For 100:
We can factorize 100 as 2 x 2 x 5 x 5, which can be written as 2^2 x 5^2.
For 126:
We can factorize 126 as 2 x 3 x 3 x 7, which can be written as 2 x 3^2 x 7.
For 250:
We can factorize 250 as 2 x 5 x 5 x 5, which can be written as 2 x 5^3.
Now, we will multiply together the highest powers of all the prime factors:
2^2 x 3^2 x 5^3 x 7 = 4 x 9 x 125 x 7 = 25200.
Therefore, the LCM for the set of numbers 100, 126, and 250 is 25,200.