what are all the common multiples of 12 and 15

Question

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

Answer 1

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!

Answer 2

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!

Answer 3

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.

60, 180, 240, 300, 360, ...60+n(60) where n = any integer

or 60n where n= any integer >0

that's an infinite number of common multiples, no matter how you slice them

Answer 4

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.

Answer 5

If you have two numbers a and b and you want to find the least common multiple of it you can use the formula:

( a times b )/ least common factor of a and b.

for your question it will be (12*15)/3=60.

Answer 6

Using prime number factorization is the best approach since lists of multiples are not practical for large numbers. Divide 12 by the first prime number. 2. The quotient is 6.

DIvide the quotient, 6, by 2 again. That results in 3. 3 cannot be divided by 3. In fact, it is prime, so you cab stop. 2×2×3=12, so we now have the prime factorization of 12.

15 is odd, so you can't divide by 2 without getting a remainder. Try the next prime, and the quotient is 5. 5 is prime, so you can stop.

15=3×5.

Starting with the prime factor 2, write down all the factors in each factorization, but only once and using the most factors. This would be 2×2 first, 3 next, then 5.

Multiply them all together 2×2×3×5=60. 60 is the least common multiple.

For a list of more common multiples, simply multiply 60 by 1, 2, 3, 4 etc. All common multiples of 12 and 15 MUST be multiples of 60.

Answer 7

Find all the common multiples of 12 and 15

First, I would determine the LCM of 12 and 15.

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

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

I notice there is a pattern for each set of multiples.

Examples:

12 x 5 = 60

12 x 10 = 120

12 x 15 = 180

12 x 20 = 240

OR

60(2) = 120

60(3) = 180

60(4) = 240

Next,

15 x 4 = 60

15 x 8 = 120

15 x 12 = 180

15 x 16 = 240

OR

60(2) = 120

60(3) = 180

60(4) = 240

You can use this strategy until you know ALL the common multiples of 12 and 15, which are endless. So, as a teacher, I would give students a stopping point.

Answer 8

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.

Answer 9

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.

Answer 10

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.