I need help with finding the LCM (lowest common multiple).?

Question

I am not stupid. But I have had conflicting help with it.

And I'm worried that if I do not do it this week, my Maths teacher will begin to hate me.

=(.

So a well staged example would be extremely grateful.

Thanks.

LCM - I need an easy example. It has to be written using prime factors.

Thanks.

Answer 1

Here's a rule and an example after for clarity.

To find the LCM of n1 and n2, first factor the numbers into their prime factorizations like this:

n1 = (2^a) (3^b) (5^c)x(7^d) x ... x (prime^(exp) x ...
and
n2 = (2^A) (3^B) (5^C)x(7^dD x ... x (prime^(EXP) x ...

where a, A, b, B, c, C, ... could be zero powers.

Let m(x,y) = the lareger value of x & y.

then,

LCM = (2^m(a,A)) x (3^m(b,B)) x (5^m(c,C))x(7^m(d,D)) x ...

EXAMPLE:
Find the LCM of 44 and 120.

44 = 2^2 x 11^1
120 = 2^3 x 3 x 5

LCM = 2^m(2,3) x 3^(0,1) x 5^m(0,1) x 11^(1,0)

LCM = 2^3 x 3^1 x 5^1 x 1^1

LCM = 8 x 3 x 5 x 11 = 1320

Answer 2

From the internet.
The smallest common multiple of two or more numbers is called the lowest common multiple (LCM).
E.g. Multiples of 8 are 8, 16, 24, 32, …
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, …




In general:
To find the lowest common multiple (LCM) of two or more numbers, list the multiples of the larger number and stop when you find a multiple of the other number. This is the LCM.


Example 3
Find the lowest common multiple of 6 and 9.

Solution:
List the multiples of 9 and stop when you find a multiple of 6.

Multiples of 9 are 9, 18, …
Multiples of 6 are 6, 12, 18, …




Example 4
Find the lowest common multiple of 5, 6 and 8.

Solution:
List the multiples of 8 and stop when you find a multiple of both 5 and 6.

Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, …

Stop at 120 as it is a multiple of both 5 and 6.

So, the LCM of 5, 6 and 8 is 120.

Answer 3

The idea is that we are calculating a number that is a multiple of each in the sample set. Most straightforward way is to divide each member of the set into its prime components, and then to use a multiple of each prime so as to satisfy the composition of the original numbers. As an example, find the LCM of 16, 24, and 30:
16 = 2 * 2 * 2 * 2
24 = 2 * 2 * 2 * 3
30 = 2 * 3 * 5.
We need four 2's (from 16, and the 3 2's in 24, and one 2 in 30 satisfy)
We need one 3 (in each of 24 and 30)
We need one 5 (from 30).
This gives us 2 * 2 * 2 * 2 * 3 * 5 = 240, the LCM of these numbers.

Answer 4

Have a look at this site:

http://en.wikipedia.org/wiki/Least_common_multiple

The easiest way I can think to show how to do this is to start listing multiples of your two numbers until you hit a match. Of course, this is going to get tedious if you have to list out more than a few multiples. In that case, check out that site for the formulas they give. For an easy example, let's try 5 and 8.

5, 10, 15, 20, 25, 30, 35, 40
8, 16, 24, 32, 40

40 is a match and will be the LCM

Answer 5

In finding the LCM, you are looking for a number that both numbers can go into. For example, let's take 4 and 6. The number 4 can go into 4, 8, 12, 16, 20, 24...........(think timetables) The number 6 can go into 6, 12, 18, 24, 30....... (think timetables). Now see if both numbers (4,6) have common multiples. The common multiple are 12,24. 12 is the lowest common multiple because it is the lowest number.

Hope this helps.

Answer 6

Well, the Lowest Common multiple is the lowest equation between two different numbers. Take 4 & 5 for example. The Lowest common multiple would be 20, as the multiples of 4 are 4,8,12,16,20 and the multiples of 5 are 5,10, 15, 20. The lowest one they have in common is 20. The lowest common multiple can also be one of the numbers asked. Such as in this example : 3 & 9. The lowest common multiple would be 9.

Answer 7

If you are ,say, looking for the LCM for these numbers: 24,16,30
You divide these numbers by prime numbers till all the answers are 1,1,1. Do you know what prime numbers are? They are numbers which cannot be divided by any other number except by itself: like 2,3,5,7. So 24,16,30 are divided by 2 and you get
12,8,15 and you divide by 2 again and get 6,4, but 15 cannot be divided by 2 exactly. It has a remainder. The numbers must be divided exactly with no remainder. So, you just write 15 next to your latest answers. You divide 6,4,15 by 2 again and get 3,2, 15 . Divide by 2 again and get 3 (cannot divide exactly so write the number down,) 1, 15 and now divide this by 3 and get 1,1 (bring down the 1) and 5 and last ,divide by 5 and now you get 1,1,1. Now multiply all the numbers you had used to divide (Prime numbers you used)& your answer is 240.It is difficult to teach you like that with no symbols I hope you get the understanding you need.

Answer 8

well if they ask you for a lowest common mutiple of 6 and 8 it would be 2 because if you do it out 1 2 3 6 one time 6 is 6 and 2 tiem 3 is 6 and 1 2 4 8 one time 8 is eigth and 2 time 4 is also 8 . so you find the number that 6 and 8 have in common which is 2. so 2 is your answer. get now? good luck.

Answer 9

consider:3,4,2
there are many numbers eg.12,24..and....we can divide by 3,4,2.
12 is the smallest.(lcm)