Question

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

Answer 1

12

Explanation:

Think of it this way. Simplifying 3, 4 and 6 into their simplest factors:

`3=3`

`4=2*2`

`6=3*2`

6 is a multiple of both 3 and 2, which are both represented by the factors of 3 and 4. Thus, as it is doubled in these, it is not necessary to find the lowest common multiple of the numbers.

Now the LCM can be multiplied with the factors of the remaining numbers:

LCM
`=3*2*2`

Notice the first two numbers equal 6, the second and third equal 4, and the first only equals 3. This means the three numbers are represented in the LCM.

`3*2*2=24`

And that is the LCM, so we are done. QED

Answer 2

12

Explanation:

Write down multiples of each number:

3, 6, 9, 12 . . .

4, 8, 12 . . .

6, 12 . . .

The first one they all have is the LCM.