What is the least common multiple of 15 and 12 and 9?

Answer 1

The LCM of 9, 12 and 15 is 180.

3 x 3 = 9

2 x 2 x 3 = 12

3 x 5 = 15

2 x 2 x 3 x 3 x 5 = 180, the LCM

Method 1:

The easy to explain way is to look at the multiples of the largest number (15) and then see which is the first one to also divide evenly by both other numbers. This can be a little tedious though.

So the multiples of 15 are 15, 30 , 45 etc.. up to 180(the first which is also a multiple of both 9 and 12).

Method 2:

The second approach, whilst more difficult to explain, offers a potentially easier method when the numbers are a little awkward. You will have to excuse me if the explanation is a little lacking as I have only just considered this (for more than 2 numbers).

The relationship between 9 and 12 is a ratio of 9 to 12. If we simplify this ratio we end up with 3 to 4.

You will see that if we now multiply 9 by the 4 and the 12 by the 3 we will end up with the same answer of 36.

This would be the method to calculate the lcm of just 9 & 12 (which is 36).

However, here we also have 15. If we consider the ratio of 9 to 15 and simplify we end up with 3 to 5. So, we actually have three numbers here in the ratio of 3 to 4 to 5. To find the lcm if we now multiply the 9 by the 4 (as we did a moment ago) but then multiply the result by the 5 also, we will end up with the lcm of all three numbers.

9 * 4 * 5 = 180.
Let's list out a couple of common multiples for every number.

09 = 09, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180

12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180

15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180

As you can see, we had to list out a lot - but we found the lowest common multiple, 180.
The LCM of the given three numbers is 180

Answer 2

The least common multiple of the numbers 15, 12 and 9 is 180.

Answer 3

1,215 is, since it's already a multiple of 9 .

Answer 4

32 x 4 x 5 = 180

Answer 5

180

Answer 6

180