Question

What is the least common multiple of 8 and 14?

Answer 1

See explanation...

Explanation:

Alright, first we need to look at the what an LCM is. A least common multiple (LCM) is the lowest multiple that two or more numbers share.

For example, the numbers `2` and `8`, the LCM would be `8` based on the following set of multiples:

Multiples of `2:` 2, 4, 6, 8, 10, 12, 14,...
Multiples of `8:` 8, 16, 24, 32, 40, 48, 56,...

So lets look at the LCM of `8` and `14` now. How I like to do it is you multiply the smaller number by `2` until they are the same. They may seem confusing, let me explain.

Since `8` is the smaller of the two numbers, once we multiply that by `2` we get `16`. `16` is not equal to `14` so we keep going. To help you out, I've color coded the numbers so that `color(blue)(blue)` is a multiple of `color(blue)14` and `color(red)(red)` is a multiple of `color(red)8`

`14*2=28`
`color(blue)28!=color(red)16`

`8*3=24`
`color(red)24!=color(blue)28`

`8*4=32`
`color(red)32!=color(blue)28`

`14*3=42`
`color(blue)42!=color(red)32`

`8*5=40`
`color(red)40!=color(blue)42`

`8*6=48`
`color(red)48!=color(blue)42`

`14*4=56`
`color(blue)56!=color(red)48`

`8*7=56`
`color(red)56=color(blue)56`

Hope this helps!
~Chandler Dowd

Answer 2

56

Explanation:

To find the least common multiple find the prime factorization of each number and multiply the unique non repeated factors.

`8 = 2 xx 2 xx 2 = 2^3` There are 3 factors of 2 in 8

`14 = 2 xx 7 = 2^1 xx 7^1` There is 1 factor of 2 and 1 of 7 in 14

The 1 factor of 2 in 14 is a repeat of the 3 factors of 2 in 8. It is not
necessary to use that fourth factor of 2. three factors of 2 is enough

The 1 factor of 7 is a unique factor. The factor of 7 is necessary so

The LCM = `2 xx 2 xx 2 xx 7 = 56`

The least Common Multiple of 8 and 14 is 56