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 Post subject: lowest common multiplePosted: Tue Dec 02, 2014 10:22 am

Joined: Thu Oct 18, 2012 9:41 am
Posts: 444
wondering if there is a quick way to find the lcf of say 4,5 ,6 7,

DD multiplies them all getting 840, though this isn't the lcd

Is there a quick way to get to 420 rather than writing out all the factors of each one and seeing which ones match up?

Thanks

Last edited by SleepyHead on Tue Dec 02, 2014 11:05 am, edited 1 time in total.

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 Post subject: Re: lowest common factorPosted: Tue Dec 02, 2014 10:41 am

Joined: Fri Oct 12, 2007 12:42 pm
Posts: 3826
I think you mean lowest common multiple.
The mistake she made was with the 4 and the 6.
4 x 6 = 24 but the common multiples of 4 and 6 are 12s
She can look at the non prime numbers and use their common multiples.
12 x 5 x 7
This is a reasonably easy calculation too: 12 x 5 = 60, 6 x 7 x 10 = 420
Each time a non-prime is involved it is necessary to see where they overlap, e.g.
The common multiple of 3, 5 and 15 is 15 rather than 225.

To find this at KS3/4 students look at the prime factors:
4 (2,2), 5 (5), 6 (2,3), 7 (7)
Each prime factor that appears more than once is only counted in the biggest group. Here 2 occurs in both 4 and 6 so we keep 2 x 2 but don't use the 2 in 2 x 3
So to get the final answer
2 x 2 x 5 x 3 x 7

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 Post subject: Re: lowest common factorPosted: Tue Dec 02, 2014 10:54 am

Joined: Fri Oct 24, 2014 11:49 am
Posts: 35
There is no quick way to find a Lowest Common Multiple that works reliably for all numbers I'm afraid. Sorry.
So, as you suggest in your post sleepyhead, for 4,5,6,7 you would list the prime factors of each number with the results:
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
You then take each of these factors and include them in a long multiplication sum. If a factor occurs in more than one of the above lists only include it once. If it occurs more than once in any list list then it needs to be included more than once in the multiplication sum.
For 4,5,6,7 we have:
Lowest Common Multiple = 2 x 2 x 5 x 3 x 7 = 420.

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 Post subject: Re: lowest common multiplePosted: Tue Dec 02, 2014 11:04 am

Joined: Thu Oct 18, 2012 9:41 am
Posts: 444
thank you - yes I did mean LCM

then

4= 2 x 2

5 = 5

6 = 2 x 3

12 = 2 x 2 x 3

So what would be the multiplication sum here, how would we treat the two 2s in 12 and also the repeated 3.

Thanks

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 Post subject: Re: lowest common multiplePosted: Tue Dec 02, 2014 11:40 am

Joined: Fri Oct 12, 2007 12:42 pm
Posts: 3826

12 has already been 'used up' by the 6 and 4.
As such each set of factors only occurs once. If your DD is only 9 or 10 then I would always concentrate on looking at pairs of factors before going on to the abstract that we are covering here.
A factor only counts once (unless like with 4 it, in this case 2, occurs more than once in a number).

The common multiple of 2 and 6 is 6 because
2 (2)
6 (2 x 3)
We have used the first 2 in the 2 and don't need it in the 6
so we are left with 2 x 3

4, 6, 12
4 (2 x 2)
6 (2 x 3)
12 (2 x 2 x 3)
The first 2 can be crossed off the other numbers
4 (2 x 2)
6 (3)
12 (2 x 3)
The second 2 can then be crossed off the other numbers
4 (2 x 2)
6 (3)
12 (3)
All the prime factors from 4 are used up
Next we can cross out the 3 from 6
4 (2 x 2)
6 (3)
So we are left with
2 x 2 x 3 = 12

I hope the colour helps with the elimination process.

Taking this to your list of 4, 5, 6, 12
4 (2 x 2)
5 (5)
6 (2 x 3)
12 (2 x 2 x 3)
Cross out the first two from all numbers exept 4
Cross out the second two from all numbers except 4
Only one five - no crossing out necessary
Cross out the three from all numbers except 6
We are left with
2 x 2 x 5 x 3 = 60

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 Post subject: Re: lowest common multiplePosted: Tue Dec 02, 2014 11:54 am

Joined: Thu Oct 18, 2012 9:41 am
Posts: 444
great got it.

thanks

so in the question that DD did different light houses flashed every 4,5,6,7 seconds starting at midnight, At what time did all the light houses flash at the same time

In an exam uf DD listed all the common factors she;d be there for ages.. should I teach her this method. She's sitting her 11+ in January

thanks
SH

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 Post subject: Re: lowest common multiplePosted: Tue Dec 02, 2014 12:15 pm

Joined: Fri Oct 12, 2007 12:42 pm
Posts: 3826
It depends on her. If she likes abstract numbers then teach her the prime factor method. If she prefers something that is intuitive then teach her to look for non primes and see if they overlap with the other numbers such as the 4 and 6 which both go into 12.

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 Post subject: Re: lowest common multiplePosted: Tue Dec 02, 2014 2:33 pm

Joined: Sat Dec 03, 2011 3:14 pm
Posts: 688
we were taught to do it in one step (ancient method!)

Using a long 'L' or upside down division 'bus-stop put all the numbers in it so 4, 5, 6 and 7 would be written (due to lack of a long 'L', I'm using a '/' sign for demonstrating division. All numbers are divided and any left-overs or undivided numbers are carried over)

4, 5, 6, 7 / 2

2, 5, 3, 7 / 2

1, 5, 3, 7 / 3

1, 5, 1, 7 / 5

1, 1, 1, 7 / 7

1, 1, 1, 1

(then take all the divisors and multiply them) 2 X 2 X 3 X 5 X 7 = 420.

L.C.M of 42, 50, 45, 12 could be worked out as follows -

42, 50, 45, 12 / 2
21, 25, 45, 6 / 2
21, 25, 45, 3 / 3
7, 25, 15, 1 / 3
7, 25, 5, 1 / 5
7, 5, 1, 1 / 5
7, 1, 1, 1 / 7
1, 1, 1, 1

L.C.M = 2 x 2 x 3 x 3 x 5 x 5 x 7 = 6300

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 Post subject: Re: lowest common multiplePosted: Tue Dec 02, 2014 3:38 pm

Joined: Fri Oct 12, 2007 12:42 pm
Posts: 3826
Forgotten that method!
I use 'trees' a lot with children to find prime factors but cannot draw them on here.
The division method achieves the same thing and is much tidier.

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 Post subject: Re: lowest common multiplePosted: Tue Dec 02, 2014 6:48 pm

Joined: Thu Oct 18, 2012 9:41 am
Posts: 444
Thanks for all your replies - explained both methods to Dd and she's understood them.

Finally if dd uses a method that is not on the ks2 syllabus in an exam , would she be penalised ?

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