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

**LCM and GCF**

There are many reasons that make maths 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 divisor (lcm). Many students don’t care about these basics when there is an appropriate time to learn these basic math skills.

After reading this article, students who do not have the knowledge of least common multiple and greatest common factor can better understand these skills and can apply this knowledge to higher math concepts such as solving fractions or algebraic expressions.

**LCM:**

If students know the times tables, they can find multiples of a number quite easily, since the 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 smallest of them all. The least common multiple of the two numbers is called the least common multiple.

For example; consider that we want to find “mcm” of the numbers “6” and “8”. To find “mcm” of these numbers, write the first 5 multiples of both 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 of both, which is “24”. There is no other multiple less than 24 that is common to the two given numbers.

So “24” is the “mcm” of “6” and “8”.

Sometimes there is no common multiple in the first five multiples of the two numbers, in which case write the next five multiples to find the least common multiple.

**Greatest common factor (gcf):**

Similar to “mcm”, the most important common factor is another key skill that students must understand from the core. To find the greatest common factor of two numbers, students must find all the factors of the two numbers and then the greatest common factor is called the greatest common divisor or gcf.

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

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

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

If we look at all the factors of both the 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 with gcc and gcc to gain more confidence 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 to ensure that children have learned the basic math concepts before upgrading to learn higher math.

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