Question

what are all the common multiples of 12 and 15

Answer 1

STEP 1: determine the lowest common multiple of 12 and 15.

 

 

 

  12 15

 

1 12 15

 

2 24 30

 

3 36 45

 

4 48 60

 

5 60

 

 

 

 

 

It turns out, the lowest common multiple of 12 and 15 is 60.

 

My observation is it took five multiples of 12 and four multiples of 15 to reach the common multiple of 60 for both 12 and 15.

 

 

 

STEP 2: find the next common multiple

 

 

 

With this in mind, we can jump to the next common multiple of 12 and 15

 

60 + 12(5) = 120 & 60 + 15(4) = 120

 

 

 

 

 

STEP 3: visualize it with a table to prove that no common multiple exists between 60 and 120

 

 

 

        12 15

 

1 12 15

 

2 24 30

 

3 36 45

 

4 48 60

 

5 60 75

 

6 72 90

 

7 84 105

 

8 96 120

 

9 108

 

10 120

 

 

 

 

 

Now to answer your question of finding all common multiples of 12 and 15.

 

I'll assume five is adequate, then you can find as many as you wish beyond that.

 

 

 

There are three ways to proceed: continue making the table, an easier way, and an even easier way. We'll proceed the easier ways

 

 

 

STEP 4.a: answer the question the easy way

 

 

 

12(5x1) = 60 15(4x1) = 60

 

12(5x2) = 120 15(4x2) = 120

 

12(5x3) = 180 15(4x3) = 180

 

12(5x4) = 240 15(4x4) = 240

 

12(5x5) = 300 15(4x5) = 300

 

 

 

STEP 4.b: answer the question the even easier way

60(1) = 60

 

60(2) = 120

 

60(3) = 180

 

60(4) = 240

 

60(5) = 300

 

 

 

CONCLUSION:

 

The common multiples of 12 and 15 are simply the multiples of their lowest common multiple, 60.

60