lowest common multiple

[moved]

Not in 11+

[SleepyHead]

thank you

[ConcernedDad]

Method suggested by LMM (leanmeanmum) about LCM is what I learned a long while ago. To work it out faster, I would suggest to stop dividing if there are no further common factors among the list.

E.g.
(4, 5, 6, 7) / 2
(2, 5, 3, 7)

LC Division can be stopped at the second step as all numbers are in the second line are prime numbers and different from each other. In other words, use a divisor only if it can be used to divide more than one number in the list.
LCM would be product of all numbers in the last line, along with the divisor(s) i.e. 2 x 2 x 5 x 3 x 7 = 420

In other words, use a divisor only if it can be used to divide more than one number in the list.

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

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

LCM would be 2 x 3 x 5 x 7 x 5 x 3 x 2 = '2 x 5' x '2 x 5' x '3 x 3' x 7 = 6300

DCs probably need a bit of practice to get comfortable with this method.

[Guest55]

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

start with largest number

50 = 2 x 5 x 5

45 = 3 x 3 x 5 we already have a factor of 5 so need 3 x 3

42 = 2 x 3 x 7 we already have factors of 2 and 3 (from above) so need 7

12 = 2 x 2 x 3 we already have one 2 and 3 so we need another 2

LCM = 2 x 5 x 5 x 3 x 3 x 7 x 2

then reorder if you want to give a perfect answer.

[leanmeamum]

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

start with largest number

50 = 2 x 5 x 5

45 = 3 x 3 x 5 we already have a factor of 5 so need 3 x 3

42 = 2 x 3 x 7 we already have factors of 2 and 3 (from above) so need 7

12 = 2 x 2 x 3 we already have one 2 and 3 so we need another 2

LCM = 2 x 5 x 5 x 3 x 3 x 7 x 2

then reorder if you want to give a perfect answer.

In my own calculation I re-ordered them as follows - 2 x 5 x 2 x 5 x 3 x 3 x 7

but I thought all the shuffling up of numbers might result in a number missed out by DC

[SleepyHead]

I do like the upside down division method - DD understood the prime factor trees, but was more error prone after the point of finding all the prime factors.

For the 'upside down division method' do you always have to divide by a prime factor?


Thanks LCM questions are suddenly a lot quicker!

[ConcernedDad]

I do like the upside down division method - DD understood the prime factor trees, but was more error prone after the point of finding all the prime factors.

For the 'upside down division method' do you always have to divide by a prime factor?


Thanks LCM questions are suddenly a lot quicker!

Yes. They need to be prime factors. Better to start with 2,3 then go on to 5,7, 11 and maybe 13. They don't need to go beyond that usually.

[leanmeamum]

For the 'upside down division method' do you always have to divide by a prime factor?

yes it is better to.

9, 12, 36 / 9
1, 12, 4 / 4
1, 3, 1 / 3
1, 1, 1

LCM = 9 x 4 x 3 = 108 which would be wrong

the correct answer would be

9, 12, 36 / 3
3, 4, 12 / 3
1, 4, 4 / 2
1, 2, 2 / 2
1, 1, 1

3 x 3 x 2 x 2 = 36

(although you could substitute the 2s with a 4 but it is better not to confuse the DCs)

[Guest55]

Whichever method is used it's more important to understand the significance of LCM and how it helps in problem solving!

[SleepyHead]

thank you -will let DD know to use only prime factors