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

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??

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,206

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)*

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You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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

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

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,206

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

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
- Posts: 975

or simply "1980 and all its multiples"

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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 27
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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)*

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