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Least common multiple and fraction learning ?

Hello,

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I need help with the concept of least common multiple(s) with our SingaporeÂ math work.

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I just go up the multiples in my head until I find one in common with both denominators - but I suspect Â Â Â that some of you sassy ladies have a better way.

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There's a lovely little algorithm that's taught in some of the Singapore programs. You start by putting the two numbers at the top of two columns. Then you factor them both, creating columns as you go. For instance, as a first step you might recognize that 3 goes into both 24 and 18, so write it in a left-most column:

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Â  Â |Â 24 | Â 18Â Â

3 Â | Â  Â | Â  Â

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And then factor out the numbers and write the answers:

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Â  Â |Â 24 | Â 18Â Â

3 Â | Â 8 | Â  6

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Carry on. You'll see that 2 goes into both 8 and 6, so do that next:Â

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Â  Â |Â 24 | Â 18Â Â

3 Â | Â 8 | Â  6

2 Â | Â 4 | Â  3

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Sometimes you can only factor one of the two numbers in a given row. For instance, the 4 above can be factored by 2, but the 3 can't be. So you just leave the 3, carrying it down to the next row.

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Â  Â |Â 24 | 18Â Â

3 Â | Â 8 | Â 6

2 Â | Â 4 | Â 3

2 Â | Â 2 | Â 3
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And you just carrying on, factoring one or both columns a row at a time until you have both factored down to 1. So you can put one 2 into 2, carrying the 3 down. And then you can put one 3 into the 3.

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Â  Â |Â 24 | 18Â Â

3 Â | Â 8 | Â 6

2 Â | Â 4 | Â 3

2 Â | Â 2 | Â 3

2 Â | Â 1 | Â 3

3 Â | Â 1 | Â 1

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Once you've worked both your starting numbers down to 1's, you're done with the factoring. Your Lowest Common Multiple is all the factors in the left-most column multiplied together: 3 x 2 x 2 x 2 x 3 = 72.

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You don't necessarily need to use prime factors. For instance, you might have noticed that 6 goes into both numbers at the beginning, and then you could have factored 4 into the 4, rather than putting 2 in twice:Â

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Â  Â |Â 24 | 18Â Â

6 Â | Â 4 | Â 3

4 Â | Â 1 | Â 3

3 Â | Â 1 | Â 3

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You end up with the same result (6 x 4 x 3 = 72).Â

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The whole process seems a little unwieldy with smallish numbers, but with larger numbers (say, 84 and 294) it figures out LCMs you can't easily do in your head.Â

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Miranda

Wow Miranda - you are like my "Shell Answer Man" lately....(remember him?)... can you move into my house? Â I have a cute baby to snoogle....... :)

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Thanks!

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