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Lcm maths

Hello! I generally need help, if you do not have anything nice to say, do not say it all. Thank you for your cooperation. :smile:

Lowest Common Multiple -

there are several ways in which one could work the LCM, but all the instructions, textbooks, revision guides, BBC bitesize, maths watch, seem quite unclear.

Can someone explain really clearly how I could work out the LCM using prime factors?
The textbook gave an awful example:

find the highest power of each prime factor that appears in either list,
so the author says it would be 2**3 and 3, although 7 was one of the prime factors. He picked two numbers that clearly are not the largest because 7 would be?

Can I just have a clear tactic please?
Thank you for reading.
venn diagram.png Pop it all in a Venn diagram. Please ask me if it's unclear. I'm sleepy. :tongue: happy mathing lovely
Original post by melissadh
Hello! I generally need help, if you do not have anything nice to say, do not say it all. Thank you for your cooperation. :smile:

Lowest Common Multiple -

there are several ways in which one could work the LCM, but all the instructions, textbooks, revision guides, BBC bitesize, maths watch, seem quite unclear.

Can someone explain really clearly how I could work out the LCM using prime factors?
The textbook gave an awful example:

find the highest power of each prime factor that appears in either list,
so the author says it would be 2**3 and 3, although 7 was one of the prime factors. He picked two numbers that clearly are not the largest because 7 would be?

Can I just have a clear tactic please?
Thank you for reading.


Keep listing the multiples of each number.That's the most straight forward way but in some cases not the most efficient.

LCM of 6 and 5
5, 10, 15, 20, 25, 30, 35, 40, 45, ...
6, 12, 18, 24, 30, 36, ...

Once you find a common multiple, that's your LCM.

If the gap between two numbers is quite big; turn your attention to prime factorisation.

Alternatively, you can find the highest COMMON factor of two numbers and to achieve LCM you can divide the product of the two by this HCF.

LCM of 28 and 21

HCF of 28 and 26? That would be 2.
28⋅262=364\frac{28\cdot 26}{2}=364
(edited 7 years ago)
Reply 3
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Original post by RDKGames
Keep listing the multiples of each number.That's the most straight forward way but in some cases not the most efficient.

LCM of 6 and 5
5, 10, 15, 20, 25, 30, 35, 40, 45, ...
6, 12, 18, 24, 30, 36, ...

Once you find a common multiple, that's your LCM.

If the gap between two numbers is quite big; turn your attention to prime factorisation.

Alternatively, you can find the highest COMMON factor of two numbers and to achieve LCM you can divide the product of the two by this HCF.

LCM of 28 and 21

HCF of 28 and 26? That would be 2.
28⋅262=364\frac{28\cdot 26}{2}=364


I would like to try the alternative although it seems as though it does not work?
So for instance, the HCF of 30 and 48 is 6. If I divide it by two, it makes 3 and that is not the lowest common multiple?
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Original post by moggygeorgieee
venn diagram.png Pop it all in a Venn diagram. Please ask me if it's unclear. I'm sleepy. :tongue: happy mathing lovely

Thank you so much, regardless of your state, you still perform amazingly and explain well. I finally understand it! I've written it on a poster, my book, everywhere lest I forget this technique. Thank you again.
Reply 5
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Thank you all for your help,
I got it.
Much appreciated,
Melissa
Original post by melissadh
I would like to try the alternative although it seems as though it does not work?
So for instance, the HCF of 30 and 48 is 6. If I divide it by two, it makes 3 and that is not the lowest common multiple?


You misunderstood. Yes the HCF of 30 and 48 is 6. So now multiply 30 by 48 and then divide this product by 6.
(edited 7 years ago)
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Amazing! Thank you so much!
Reply 8
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Original post by RDKGames
You misunderstood. Yes the HFC of 30 and 48 is 6. So now multiply 30 by 48 and then divide this product by 6.


HCF is 3. :wink:
----------------------------------------------------
Yes, everyone point and have a good laugh about it, I hope you get a kick out of it.
(edited 7 years ago)
Original post by B_9710
HCF is 3. :wink:


Nope. 5*6=30 and 8*6=48
Reply 10
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Original post by RDKGames
Nope. 5*6=30 and 8*6=48


Omfg. It's been a long day.
Original post by B_9710
HCF is 3. :wink:
----------------------------------------------------
Yes, everyone point and have a good laugh about it, I hope you get a kick out of it.

That is my mistake, I meant 6 for the HCF. I'm rather tired.
Original post by melissadh
Thank you so much, regardless of your state, you still perform amazingly and explain well. I finally understand it! I've written it on a poster, my book, everywhere lest I forget this technique. Thank you again.


That's okay!! LCM and HCF can annoy me sometimes too.

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