How to find the LCM by prime factorization?

Answer 1

Example: 30 and 42

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF

Combine the factors, eliminating duplicates.

2 x 3 x 5 x 7 = 210, the LCM

Answer 2

You keep on multiplying until you find a multiple that is in all the prime factors you are multiplying.

or

Example: 30 and 42
Factor them.
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Combine the factors, eliminating duplicates.
2 x 3 x 5 x 7 = 210, the LCM

Answer 3

The LCM is the product of all the prime factors of the numbers to their greatest power. To find the LCM of a group of numbers, 27, 30, 12, and 8, for example, first find their prime factors:

Prime factors of 27 are 33

Prime factors of 30 are 2 x 3 x 5

Prime factors of 12 are 22 x 3

Prime factors of 8 are 23

The LCM of 27, 30, 12, and 8 is 23 x 33 x 5 = 8 x 27 x 5 = 1,080

Answer 4

Here is what you do. Let's take the following three numbers: 12, 15, and 18.

Using prime factorization, the factors for each number are, as follows:

12 => 2 * 2 * 3

15 => 3 * 5

18 => 2 * 3 * 3

Now, these can be rewritten, as follows:

12 => 2 squared * 3

15 => 3 * 5

18 => 2 * 3 squared

For GCF, you take the LOWEST power of the SHARED factors. So, for this problem, the only shared factor is 3.

2 is not a factor of 15 and 5 is not a factor 12 or 18. However, 3 is a factor for ALL THREE numbers.

However, for 15, the factor is 3 and for 18, the factor is 3 squared (or 9). For the GCF, you take the LOWEST power, which would be 3.

So, the GCF for 12, 15, and 18 is 3.

For LCM, you take the HIGHEST power of EACH factor. For this example, you take the highest powers for the 2, 3, and 5 factors. That would be 2 squared (or 4), 3 squared (or 9), and 5. Multiple these three factors together to get 180.

So, the LCM for 12, 15, and 18 is 180.

Answer 5

Example: 30 and 42

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Combine the factors, eliminating duplicates.

2 x 3 x 5 x 7 = 210, the LCM

Answer 6

Example: 30 and 42
Factor them.
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Combine the factors, eliminating duplicates.
2 x 3 x 5 x 7 = 210, the LCM