How do you find the greatest common factor and least common multiple?

Answer 1

To find both the least common factor and greatest common factor of given numbers:

1. List the factors of the given numbers.

2. Compare the factors and list the factors that are common to all the given numbers.

3. The largest is the greatest common factor and the smallest is the least common factor.

This means the least common factor is 1.

Additional links with information on finding the greatest common factor are provided in the "Related Questions" section below. Also is a link to a question on the least common factor.

Examples:

Compare 16 and 24.

The factors of 16 are 1, 2, 4, 8, and 16.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

The common factors are 1, 2, 4, and 8.

The least common factor is 1; the greatest common factor is 8.

Compare 6 and 35.

The factors of 6 are 1, 2, 3, and 6.

The factors of 35 are 1, 5, 7, and 35.

The only common factor is 1.

The least common factor is 1; the greatest common factor is 1.

Compare 15 and 50.

The factors of 15 are 1, 3, 5, and 15.

The factors of 50 are 1, 2, 5, 10, 25, and 50.

The common factors are 1 and 5.

The least common factor is 1; the greatest common factor is 5.

Answer 2

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF

Select the highest amount of each factor.

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

Check it.

30 x 42 = 1260

210 x 6 = 1260

It checks.
Example: 30 and 42

Factor them.

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
Example: 30 and 42
Factor them.
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
Check it.
30 x 42 = 1260
210 x 6 = 1260
It checks.

Example: 30 and 42

Factor them.

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 3

The greatest common factor, or GCF, is the largest positive integer that will divide evenly with no remainder into all the members of a given set of numbers. The least common multiple, or LCM, is the smallest positive integer that all the members of a given set of numbers will divide into evenly with no remainder.

Answer 4

Several methods are possible.1) The most primitive method - and not very efficient - is to compare all factors of two or more numbers. For the multiples, compare different multiples, until you find a common multiple.

2) The method commonly taught in school is to factor the numbers into prime factors, and look for common factors (for greatest common factor) or factors that appear at least once (for the least common multiple). If one Prime number appears more than once in some numbers, for example 2 to the power 3 versus 2 to the power 2, use the least of the powers (for the gcf) or the greatest (for the lcm).

3) Euclid's algorithm is much more efficient for larger numbers. For example: find the gcf of 14 and 10. This is the same as the gcf of 10 and 4 (4 is the remainder of the division of 14 by 10); which is the same as the gcf of 4 and 2 (again, 2 is the remainder of the division); which is the same as the gcf of 2 and 0 (0 again is the remainder). The gcf of any number and zero is the first number, in this case, 2.

To find the lcm, use the fact that a x b = gcf(a, b) x lcm(a, b). In this example, you can multiply 14 x 10, and divide the result by the gcf, which is 2.

Answer 5

List all the factors both numbers have and find the one with the most value

Answer 6

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF

Answer 7

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors and multiply them together.

2 x 3 = 6, the GCF

Answer 8

The least common factor of any set of integers is 1.