What is the least common multiple of 12 15 and 28?

Answer 1

LCM of 12 15 and 28 is 420.

You are looking for a number which is in the 12 times table, the 15 times table, and the 28 times table.

The easiest, but long, way of doing this is to write all of the numbers out. So...

12, 24, 36, 48, 60

15, 30, 45, 60

60 is a common multiple of 12 and 15, but it is not a multiple of 28 (60/28 = 2.14), so we must continue...

12, 24, 36, 48, 60, 72, 84, 96, 108, 120

15, 30, 45, 60, 75, 90, 105, 120

Again, 120 is a common multiple, but it is not a multiple of 28 (120/28 = 4.29)

You need to keep going until you reach a multiple shared by all 3 numbers, in this case it is 420

You can also reach this number by multiplying the 2 highest numbers (15 x 28 = 420), and this will give you a multiple of 15 and 28, but it may no be a multiple of the other number, and even if it is, it may no be the LOWEST common multiple.

I always use the long way because it is seemingly impossible to go wrong.

* * * * *

There is another systematic method and that is using prime factorization. The prime factorization for any number is to list all the primes that go towards making up that number. So

12 = 2*2*3

15 = 3*5

28 = 2*2*7

Now, find the maximum number of times each prime occurs in any one row, and multiply together. This method works much more efficiently if the primes are in ascending order.

Then, the answer is:

2*2 (from 12 or 28) *3 (from 12 or 15) *5 (from 15) *7 (from 28)

= 2*2*3*5*7 = 420