Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2011-02-27 03:29:40

lorynjane
Member
Registered: 2011-02-27
Posts: 13

### Common Multiples of 9, 10, 11, and 12?

I have a homework that i am really stuck with!
Does anyone know what all of the common multiples of 9, 10, 11 and 12 please??

Offline

## #2 2011-02-27 04:05:13

bob bundy
Registered: 2010-06-20
Posts: 8,421

### Re: Common Multiples of 9, 10, 11, and 12?

hi lorynjane

Multiple = another way of saying in that times table.

so multiples of 9 = { 9, 18, 27, 36, 45, ........ }

and multiples of 10 = { 10, 20, 30, 40, ........}

These lists go on for ever so you cannot list them all but you can give enough to show you know how to get them.

So how to get the common multiples?

That means they've got to be in all the lists.

hhmmm.  9,10, 11 and 12.

Well a common multiple only has to end in zero to be in the tens.

11 is a prime number (do you know what that is?)

so for 10 and 11 = {110, 220, 330, 440, .....}

Now 9 doesn't share any factors with 10 nor with 11 so the lowest number in the above list that is in the 9 times table will be 990.

so now we have

9, 10 and 11 = {990, 1980, 2970, 3960, ......}

If 12 goes into those we have our list.  Well it doesn't go into 990.  So we need to find the first number in that list that is divisible by 12.

Time for you to do some work.  Got a calculator?  Find the first number from the above list that is in the 12 times table.  Then the next, and after that they carry on in a simple way.

Post back when you have an answer.

Bob

Last edited by bob bundy (2011-02-27 04:07:53)

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!

Offline

## #3 2011-02-27 04:10:56

lorynjane
Member
Registered: 2011-02-27
Posts: 13

### Re: Common Multiples of 9, 10, 11, and 12?

The common multiple is 1980, cause it doesn't go into 990 but it goes into that! Thankyou

Offline

## #4 2011-02-27 04:27:59

bob bundy
Registered: 2010-06-20
Posts: 8,421

### Re: Common Multiples of 9, 10, 11, and 12?

Yes, you've got it, well done!

Now, just to be a show off and really impress your teacher:

all of the common multiples

find the next and the next and the next and then say, "and so on ......."

Bob

Last edited by bob bundy (2011-02-27 04:28:33)

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!

Offline

## #5 2017-11-22 15:53:40

Monox D. I-Fly
Member
From: Indonesia
Registered: 2015-12-02
Posts: 1,302

### Re: Common Multiples of 9, 10, 11, and 12?

or simply "1980 and all its multiples"

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

Offline

## #6 2017-11-24 05:18:56

Alg Num Theory
Member
Registered: 2017-11-24
Posts: 339
Website

### Re: Common Multiples of 9, 10, 11, and 12?

lorynjane wrote:

I have a homework that i am really stuck with!
Does anyone know what all of the common multiples of 9, 10, 11 and 12 please??

The common multiples of 9, 10, 11, 12 are the multiples of their lcm (lowest common multiple).

To work out their lcm, first note that 9, 10, 11 are coprime so their lcm is simply their product: lcm(9,10,11) = 9 × 10 × 11 = 990.

Now we work out the lcm of 990 and 12. This is equal to their product divided by their gcd (greatest common divisor). We have gcd(990,12) = 6. Hence lcm(990,12) = (990×12)/6 = 1980.

Last edited by Alg Num Theory (2017-11-24 07:07:36)

Offline