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## Greatest Common Fractor (gcf) And Least Common Multiple (lcm)

**LCM and GCF**

There are many reasons why math is a difficult and most hated subject among average students. One of the most important reasons is insufficient knowledge of basic mathematical concepts such as least common multiple (lcm) and greatest common factor (gcf). Many students don’t care about these basic concepts when there is a good time to learn these basic math skills.

After reading this article, students who lack the knowledge of least common multiple and greatest common factor can better understand these skills and they can apply this knowledge in higher mathematical concepts, such as solving fractions or algebraic expressions.

**Least common multiple (LCM):**

If students know multiplication tables, they can find multiples of a number quite easily, because multiples are the “times” of the given number. To find the least common multiple of two numbers, students must find multiples of the two numbers and choose a common multiple that is the least of all. This least common multiple of the two numbers is called the least common multiple.

For example; consider that we want to find “lcm” from the numbers “6” and “8”. To find “lcm” of these numbers, write the first 5 multiples of the two numbers as shown below:

6 = 6, 12, 18, 24, 30

8 = 8, 16, 24, 32, 40

Now, by looking at the first five multiples of the two numbers, we can locate the lcm for both, which is “24”. There is no other multiple less than 24, which is common to both given numbers.

Therefore, “24” is the “lcm” of “6” and “8”.

Sometimes there is no common multiple in the first five multiples of the two numbers, in this case write down the next five multiples to locate the lowest common multiple.

**Greatest common factor (gcf):**

Similar to “lcm”, the greatest common factor is another key skill that students need to understand from the ground up. To find the greatest common factor of two numbers, students need to find all the factors of the two numbers, then the greatest common factor is called the greatest common factor or gcf.

For example; consider that we want to find the gcf of the numbers “12” and “32”. To find the gcf of the given numbers, write down all the factors of the given numbers as shown below:

12 = 1, 2, 3, 4, 6, 12

32 = 1, 2, 4, 8, 16, 32

Looking at all the factors of the two numbers, it is clear that the number “4” is the greatest common factor for the given numbers “12” and “32”.

Students can practice more similar problems on lcm and gcf to become more confident in these two key skills.

It is the responsibility of students to learn the right math concepts at the right time and the responsibility of educators and parents is to ensure that children have learned basic math concepts before upgrading them to learn math superior.

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