# What is the least common multiple of 3,4, and 6?

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Tarik Share
Apr 10, 2016

12

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Then teach the underlying concepts
Don't copy without citing sources
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Explain in detail...

#### Explanation:

I want someone to double check my answer

3

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Nimo N. Share
Jan 11, 2018

12

#### Explanation:

Find the least common multiple (LCM) of 3, 4, and 6.

The LCM of two or more numbers is a number whose prime-factored form contains only the prime factors of each of the numbers.

There are two methods usually taught in school, but there are several other methods that are used, some of which are faster or easier to use, but may not be as easy to understand.

Method 1:

Factor each number into primes. One (1) is not a prime number, so it is not necessary to list it.

$4 = 2 \cdot 2.$
$6 = 3 \cdot 2.$
$L C M \left(3 , 4 , 6\right) = 3 \cdot 2 \cdot 2 = 12.$

The factors of each number can be found in in the factored LCM.

Method 2.

Make a list of a few multiples of each of the numbers. Make the lists long enough that you can find one of the numbers in each of the lists. If the list is long, there may be several such numbers, but the idea is to choose the smallest one that appears in each list.

Multiples of 3: $3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , \ldots$
Multiples of 4: $4 , 8 , 12 , 16 , 20 , 24 , \ldots$
Multiples of 6: $6 , 12 , 18 , 24 , \ldots$

Now, find the smallest ( Least ) multiple that is Common in each list of Multiples,

It is easy to pick-out the number 12 from the lists as the smallest, even though there is another number, 24, which is common to each list.

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