Find the LCM of 8, 12, and 20.

The correct option is 120.

To find the Least Common Multiple (LCM) of the numbers 8, 12, and 20, we can use the prime factorization method. This method involves breaking down each number into its prime factors and then multiplying the highest powers of all prime factors involved.

First, let's find the prime factorization of each number:

For 8:
8 can be written as 2 × 2 × 2.
In exponent form, this is:
$$8=2^3$$

For 12:
12 can be written as 2 × 2 × 3.
In exponent form, this is:
$$12=2^2\times 3^1$$

For 20:
20 can be written as 2 × 2 × 5.
In exponent form, this is:
$$20=2^2\times 5^1$$

Next, to find the LCM, we identify all the unique prime factors present across the numbers, which are 2, 3, and 5. We then take the highest power of each of these prime factors:

The highest power of 2 is $2^3$ (from 8).
The highest power of 3 is $3^1$ (from 12).
The highest power of 5 is $5^1$ (from 20).

Now, we multiply these values together to get the LCM:

$$\mathrm{LCM}=2^3\times 3^1\times 5^1$$

Calculating the product:
$$\mathrm{LCM}=8\times 3\times 5$$
$$\mathrm{LCM}=24\times 5$$
$$\mathrm{LCM}=120$$

Therefore, the Least Common Multiple (LCM) of 8, 12, and 20 is 120.