Amber S.

asked • 08/26/12# what are all the common multiples of 12 and 15

well i am doing a project and need the common multiples of 15 and 12 within the next 10 min. thank you

## 7 Answers By Expert Tutors

Marcus R. answered • 09/28/21

B.S. Engineering, 10 yrs math tutor experience, patient, honest

Find all the common multiples of 12 and 15

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**.

Now, take it away!

Barry D.

04/24/22

Raymond B. answered • 04/23/21

Math, microeconomics or criminal justice

break them down, into prime factors. If it's even you know there's a factor of 2. If the digits sum to a number divisible by 3, it's divisible by 3. If it ends in a 0 or 5, it's divisible by 5. 1+2 = 3, so you know there's a factor of 3. 1+5 =6. 6 is divisible by 3, so you know 15 is divisible by 3. While you may not need this for a relatively simple problem like this, it comes in handy with bigger numbers.

12 = 3 x 2 x 2

15 = 3 x 5

3 is in common, now stick on what they don't have in common 2x2x5=20

20x3 = 60. that's the least common multiple: 60

you could just multiply them: 12x15 = 180. that's a multiple, but not the LCM, least common multiple.

Lauren B. answered • 09/04/12

Improving Dubuque's Math Skills One Student at a Time

The easiest approach to finding common multiplies is to list multiples of each number until you find what they have in common. It can take a long time, but can also be the most useful.

12: 12, 24, 36, 48,** 60**, 72, ...

15: 15, 30, 45, **60**, 75, 90...

As you can see, the least common multiple is 60. There are other quicker methods to do this, but this seems to be the easiest and sometimes is the fastest.

Barry D.

04/24/22

Here's a fun response. You invited a friend over for dinner. But you don't remember which friend. And you don't want to call and ask them because you don't want to upset the one who wasn't invited. You know what each one likes for dinner. So what do you make? Both dinners! Fortunately in this case, there's some overlap.

The first friend likes 12. What's in a 12? Well...let's break it down. 2x6 is 12. The 2 is a basic food item but 6 isn't. 6 = 2x3. So the full "12" dinner is 12 = 2x6 = 2x2x3....Two 2s and a 3.

The second friend likes 15. What goes into making a 15? 5x3...a 5 and a 3.

So what should you make for dinner so that no which friend comes over....that friend is happy? If you just make 12, you've got 2x2x3. The 15 likes 3....but there's no 5 yet in 12. So you have to make a 5 too. That means you'll make 2x2x3x5 = 60. There's a 12 in it (2x2x3)x5. And a 15: 2x2x(3x5). So there'll be extra food no matter what, but that's ok! So 60 is the Lowest Common Meal you can make to satisfy 12 and 15! I mean.....Lowest Common Multiple of 12 and 15!

Every "60" will be a multiple of 12 and 15. So 60....120....180...240....(60xN)....

Bon appetit!

Rana A. answered • 03/04/21

Tired of the school system teaching your kids to fail? Me too!

If you think of multiples as multiply, you can answer the question yourself. People get multiples and factors confused though.

So, an easy way to stop that confusion is to think of multiples as what you multiply or count multiples of.

For instance, 15, 30, 45, 60..You're MULTIPLYING, such as 15*1 = 15, 15*2 = 30, etc.

So, factors you break apart and multiples you multiply.

Multiples of 10 = 10, 20, 30, 40

Multiples of 2 =2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Common means what the two groups have in common.

For instance, the multiples of 10 and 2 have two common multiples. 10 and 20. If I kept adding numbers to the 2 multiples group, I would find more common multiples such as 30, 40, etc.

See, not so hard.

Kelly M. answered • 08/27/12

Math, Test Preparation, and More

To determine the multiple of a number multiple that number by 1, 2, 3, 4, etc. For example, the multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, etc. (5 x 1 = 5, 5 x 2 = 10, 5 x 3 = 15 and so on).

The multiples of 10 are: 10, 20, 30, 40, etc.

To find the common multiples of 5 and 10 identify the multiples that both numbers share. The common multiples would be 10, 20, 30, 40, etc. In my specific example you can say all the common multiples of 5 and 10 are equal to the multiples of 10.

If you follow the steps I showed above you can determine the common multiples of 12 and 15. Hint: By the time you reach the multiple of 300 you should have identified 5 common multiples. Also the pattern you find to identify all common multiples of 12 and 15 will be different than the pattern I showed in my example.

common multiples or common factors? Any light on what you are looking to accomplish as well? THe easiest way to answer this is to multiply the two numbers together as each one will inherit the factors.

15*12=180, thus 360, etc will be a multiple.

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Exquisite W.

Answer: LCM is the method to find the smallest possible multiple of two or more numbers. LCM stands for Least common multiple. LCM of two numbers is divisible by both the numbers. Method to find least common multiple (LCM) We can find the LCM by two ways By listing the multiples By prime factorisation LCM of 12 and 15 We can find the LCM of 12 and 15 by both the above-mentioned methods. First Method: Listing the multiples First write the common multiples of all the three numbers. Common Multiples of 12: 12,24,36,48,60,72,…. Common Multiples of 15: 15, 30, 45, 60, 75,… Hence, the Least common multiple of 12 and 15 is 60. Second method: By Prime factorisation Let us write the prime factors of the two numbers individually. 12 = 2 x 2 x 3 15 = 3 x 5 Multiply each factor the maximum number of times it occurs in either number = 2 X 2 X 3 X 5 LCM (12 and 15) = 60 Answer04/14/21