# What is the least common multiple (LCM) of 8, 12, and 18?

##### 2 Answers

#### Answer:

Least Common Multiple is

#### Explanation:

Multiples of

Multiples of

Multiples of

Hence common multiples are

and Least Common Multiple is

Another shorter way is to write numbers as multiplication of its prime factors

So maximum times is three times for

Hence, Least Common Multiple is

#### Answer:

Use Shwetyank's method in the class and an exam. The marking schema will be set up for that approach.

#### Explanation:

Target: LCM of 8,12 and 18.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3 lines inclusive of the answer for 3 relationships

///////////////////////////////////////////////////////////////////////////////////////////////

There are many ways of writing any particular value so we can make it look however we wish as long as final outcome is the correct value. Example: 6 can and may be written as

We can use this to our advantage.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Write 12 as

Now we start counting the 12's but make sure it encompasses the 8 + 4's. When we have accumulated enough 4's to make another eight we have found the least common factor of 8 and 12

So LCF (for 8 and 12) is 24

So we have a fixed ratio of 8 and 12 at every sum of 24. Consequently any other product of factors will need to include some multiple of 24

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As the value of 24 locks together the counts of 8 and 12 we carry that forward.

Write the 24 as

We are now counting the 24's

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~