Find the least common multiple of 12, 18, and 30.

6 is the greatest common factor

12*18*30=6480
Divide the product of the numbers (6480) by the greatest common factor (6)

So 6480/6=1080

Well, let's see. To find the least common multiple, I like to imagine the numbers at a party. So 12, 18, and 30 are at a party, huh? Well, first things first, they need to find a common denominator. Let's say the party theme is "Multiples."

So, 12 starts by bringing its friends: 24, 36, 48...

Next, 18 jumps in with its friends: 36, 54, 72...

And finally, 30 joins the party with its friends: 60, 90, 120...

Now, at this point, the party crasher is going to check if there's a number that all three guests have in common. Drumroll, please!

The least common multiple of 12, 18, and 30 is... 180! That's the number that makes all three guests happy and keeps the party going. So 180 would be our least common multiple.

To find the least common multiple (LCM) of 12, 18, and 30, you can use prime factorization.

Step 1: Prime factorize each number:
12 = 2 * 2 * 3
18 = 2 * 3 * 3
30 = 2 * 3 * 5

Step 2: Identify the highest power of each prime factor:
- For the prime factor 2, the highest power is 2.
- For the prime factor 3, the highest power is 3.
- For the prime factor 5, the highest power is 1 (since it only appears in 30).

Step 3: Multiply the highest powers of each prime factor together:
2^2 * 3^3 * 5^1 = 4 * 27 * 5 = 540

Therefore, the least common multiple of 12, 18, and 30 is 540.

To find the least common multiple (LCM) of 12, 18, and 30, we can use the prime factorization method.

Step 1: Prime factorize each number.
Prime factorization of 12: 2^2 * 3
Prime factorization of 18: 2 * 3^2
Prime factorization of 30: 2 * 3 * 5

Step 2: Write down each prime factor with the highest exponent.
Common prime factors: 2^2 * 3^2 * 5

Step 3: Multiply the common prime factors.
2^2 * 3^2 * 5 = 4 * 9 * 5 = 180

Therefore, the LCM of 12, 18, and 30 is 180.